{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "4b823a0b",
   "metadata": {},
   "source": [
    "# 4. Linear Models for Classification\n",
    "\n",
    "### *Table of Contents*\n",
    "* 4.1 [Discriminant Functions](#4.1-Discriminant-Functions)\n",
    "    * 4.1.3 [Least squares for classification](#4.1.3-Least-squares-for-classification)\n",
    "    * 4.1.4 [Fisher's linear discriminant](#4.1.4-Fisher's-linear-discriminant)\n",
    "    * 4.1.7 [The perceptron algorithm](#4.1.7-The-perceptron-algorithm)\n",
    "* 4.2 [Probabilistic Generative Models](#4.2-Probabilistic-Generative-Models)\n",
    "* 4.3 [Probabilistic Discriminative Models](#4.3-Probabilistic-Discriminative-Models)\n",
    "* 4.4 [Laplace Approximation](#4.4-Laplace-Approximation)\n",
    "* 4.5 [Bayesian Logistic Regression](#4.5-Bayesian-Logistic-Regression)\n",
    "    * 4.5.1 [Laplace approximation](#4.5.1-Laplace-approximation)\n",
    "    * 4.5.2 [Predictive distribution](#4.5.2-Predictive-distribution)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9f58992a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn.datasets import make_classification\n",
    "from prml.preprocessing import LinearFeature\n",
    "from prml.linear import LeastSquaresClassifier\n",
    "from prml.linear import FisherLinearDiscriminant\n",
    "from prml.linear import Perceptron\n",
    "from prml.linear import GenerativeClassifier\n",
    "from prml.linear import LogisticRegression\n",
    "from prml.linear import SoftmaxRegression\n",
    "from prml.linear import BayesianLogisticRegression\n",
    "from prml.distribution import Gaussian\n",
    "\n",
    "# Set random seed to make deterministic\n",
    "np.random.seed(0)\n",
    "\n",
    "# Ignore zero divisions and computation involving NaN values.\n",
    "np.seterr(divide=\"ignore\", invalid=\"ignore\")\n",
    "\n",
    "# Enable higher resolution plots\n",
    "%config InlineBackend.figure_format = 'retina'\n",
    "\n",
    "# Enable autoreload all modules before executing code\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db4ef7ea",
   "metadata": {},
   "source": [
    "The goal in classification is to take an input vector $\\mathbf{x}$ and assign it to one of $K$ discrete classes $\\mathcal{C}_k$, where $k=1\\dots,K$. The input space is thereby divided into *decision regions* whose boundaries are called *decision boundaries* or *decision surfaces*. Linear models define decision surfaces as linear functions of the input vector $\\mathbf{x}$ and hence are defined by $(D-1)$-dimensional hyperplanes inside the $D$-dimensional space. Datasets whose classes can be separated exactly by linear decision surfaces are called *linearly separable*.\n",
    "\n",
    "There are three distinct approaches to the classification problem:\n",
    "\n",
    "1. Discriminant functions that directly assign each input vector $\\mathbf{x}$ to a class.\n",
    "2. Models that directly learn the conditional probability $p(\\mathcal{C}_k|\\mathbf{x})$ using parametric modelling.\n",
    "3. Generative approaches that model the class conditional density $p(\\mathbf{x}|\\mathcal{C}_k)$, and the prior probabilities $p(\\mathcal{C}_k)$ for the classes. Then they derive the posterior using the Bayes theorem.\n",
    "\n",
    "In the linear regression models, the model prediction $y(\\mathbf{x}, \\mathbf{w})$ was given by a linear function of the parameters $\\mathbf{w}$. For classification problems, however, we wish to predict discrete class labels. To that end, we consider a generalization of the above model in which we transform the linear function using a nonlinear function $f(\\cdot)$ so that\n",
    "\n",
    "$$\n",
    "y(\\mathbf{x}) = f(\\mathbf{w}^T\\mathbf{x} + w_0)\n",
    "$$\n",
    "\n",
    "In machine learning, the function $f$ is known as an *activation function*."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aebbe509",
   "metadata": {},
   "source": [
    "## 4.1 Discriminant Functions\n",
    "\n",
    "A discriminant is a function that assigns one of $K$ classes to an input vector $\\mathbf{x}$. *Linear discriminants* define decision surfaces that are hyperplanes.\n",
    "\n",
    "\n",
    "### 4.1.1 Two Classes\n",
    "\n",
    "The simplest linear discriminant function is obtained by taking a linear function of the input vector so that,\n",
    "\n",
    "$$\n",
    "y(\\mathbf{x}) = \\mathbf{w}^T\\mathbf{x} + w_0\n",
    "$$\n",
    "\n",
    "where $\\mathbf{w}$ is a *weight vector* and $w_0$ is a *bias* (the negative of the bias is also called *threshold*). Then, an input $\\mathbf{x}$ is assigned to a class $\\mathcal{C}_1$ if $y(\\mathbf{x})\\geq0$ and to class $\\mathcal{C}_2$ otherwise. Thus, the decision boundary is defined by $y(\\mathbf{x})=0$.\n",
    "\n",
    "Consider two points $\\mathbf{x}_A$ and $\\mathbf{x}_B$ onto the decision surface. Then, $y(\\mathbf{x}_A)=y(\\mathbf{x}_B)=0 \\Leftrightarrow \\mathbf{w}^T(\\mathbf{x}_A-\\mathbf{x}_B)=0$, which implies that the vector $\\mathbf{w}$ is orthogonal to every vector lying in the decision surface as depicted below:\n",
    "\n",
    "<img src=\"../images/fg4_1.png\" width=\"400\"/>\n",
    "\n",
    "Note that for more than two classes ($K>2$), a *one-vs-the-rest* classifier can be used in order to avoid regions of input space that are ambiguously classified. The linear function of each class takes the form $y_k(\\mathbf{x}) = \\mathbf{w}_k^T\\mathbf{x} + w_{k0}$, and assigns a point $\\mathbf{x}$ to class $\\mathcal{C}_k$ if $y_k(\\mathbf{x}) > y_j(\\mathbf{x}) \\; \\forall j\\neq k$.\n",
    "\n",
    "In the following sections we explore three approaches to learning the parameters of linear discriminant functions:\n",
    "\n",
    "1. Least squares\n",
    "2. Fisher's linear discriminant\n",
    "3. Perceptron algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "010ca3f2",
   "metadata": {},
   "source": [
    "### 4.1.3 Least squares for classification\n",
    "\n",
    "In [Chapter 3](ch3_linear_models_for_regression.ipynb), we minimized the sum-of-squared error function led to a closed-form solution for the parameter values. Can we apply the same principle to classification problems?\n",
    "\n",
    "Consider a general classification problem having $K$ classes, using a $1$-of-$K$ binary coding scheme or *one-hot* encoding for the target vector. Each class $\\mathcal{C}_k$ is described by its own linear model $y_k$. We can group these models together using vector notation so that\n",
    "\n",
    "$$\n",
    "\\mathbf{y}(\\mathbf{x}) = \\mathbf{\\tilde{W}}^T\\mathbf{\\tilde{x}}\n",
    "$$\n",
    "\n",
    "where $\\mathbf{\\tilde{W}}$ is a matrix whose $k^{th}$ column comprises the $D+1$-dimensional vector $\\mathbf{\\tilde{w}}_k=(w_{k0},\\mathbf{w}_k^T)^T$ and $\\mathbf{\\tilde{x}}$ is the augmented vector $(1, \\mathbf{\\tilde{x}}^T)^T$. The parameter matrix $\\mathbf{\\tilde{W}}$ is determined by minimizing the sum-of-squares error function, as presented in [Chapter 3](ch3_linear_models_for_regression.ipynb). Thus, the solution for $\\mathbf{\\tilde{W}}$ is obtained from\n",
    "\n",
    "$$\n",
    "\\mathbf{\\tilde{W}} = (\\mathbf{\\tilde{X}}^T\\mathbf{\\tilde{X}})^{-1}\\mathbf{\\tilde{X}}^T\\mathbf{T}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "60bb27c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 264,
       "width": 386
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# number of training points\n",
    "N = 100\n",
    "\n",
    "x_train, t = make_classification(\n",
    "    n_features=2, n_informative=2, n_redundant=0, n_classes=2, n_clusters_per_class=1, n_samples=N\n",
    ")\n",
    "\n",
    "x1, x2 = np.meshgrid(np.linspace(-5, 5, 100), np.linspace(-5, 5, 100))\n",
    "x_test = np.array([x1, x2]).reshape(2, -1).T\n",
    "\n",
    "feature = LinearFeature()\n",
    "x_train_linear = feature.transform(x_train)\n",
    "x_test_linear = feature.transform(x_test)\n",
    "\n",
    "model = LeastSquaresClassifier()\n",
    "model.fit(x_train_linear, t)\n",
    "predicted = model.predict(x_test_linear)\n",
    "\n",
    "plt.scatter(x_train[:, 0], x_train[:, 1], c=t)\n",
    "plt.contourf(x1, x2, predicted.reshape(100, 100), alpha=0.2, levels=np.linspace(0, 1, 3))\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(-5, 5)\n",
    "plt.xlabel(\"$x_1$\", fontsize=12)\n",
    "plt.ylabel(\"$x_2$\", fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f3019b8",
   "metadata": {},
   "source": [
    "The least-squares approach gives an exact closed-form solution for the discriminant function parameters. However, even as a discriminant function (making decisions directly) it suffers from some problems. We already know that least-squares solutions lack robustness to outliers, and this applies equally to classification, as depicted in the following figure. Note that the additional outlier data points produce a change in the location of the decision boundary, even though these point would be correctly classified by the original decision boundary. The sum-of-squares error function penalizes predictions that are *too correct* in that they lie a long way on the correct side of the decision boundary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0c8d1352",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 334,
       "width": 889
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# number of training points\n",
    "N = 100\n",
    "\n",
    "# number of outlier points\n",
    "n_outliers = 5\n",
    "\n",
    "x_train, t = make_classification(\n",
    "    n_features=2, n_informative=2, n_redundant=0, n_classes=2, n_clusters_per_class=1, n_samples=N, random_state=12\n",
    ")\n",
    "\n",
    "x1, x2 = np.meshgrid(np.linspace(-5, 5, 100), np.linspace(-5, 5, 100))\n",
    "x_test = np.array([x1, x2]).reshape(2, -1).T\n",
    "\n",
    "outliers = np.random.random_sample((n_outliers, 2)) + 3\n",
    "x_train_outliers = np.vstack((x_train, outliers))\n",
    "t_outliers = np.hstack((t, np.ones(n_outliers, dtype=int)))\n",
    "\n",
    "feature = LinearFeature()\n",
    "x_train_linear = feature.transform(x_train)\n",
    "x_train_linear_outliers = feature.transform(x_train_outliers)\n",
    "x_test_linear = feature.transform(x_test)\n",
    "\n",
    "model = LeastSquaresClassifier()\n",
    "model.fit(x_train_linear, t)\n",
    "predicted = model.predict(x_test_linear)\n",
    "\n",
    "plt.figure(figsize=(15, 5))\n",
    "\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.scatter(x_train[:, 0], x_train[:, 1], c=t)\n",
    "plt.contourf(x1, x2, predicted.reshape(100, 100), alpha=0.2, levels=np.linspace(0, 1, 3))\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(-5, 5)\n",
    "plt.xlabel(\"$x_1$\", fontsize=12)\n",
    "plt.ylabel(\"$x_2$\", fontsize=12)\n",
    "plt.title(\"Original decision boundary\")\n",
    "\n",
    "model.fit(x_train_linear_outliers, t_outliers)\n",
    "predicted_outliers = model.predict(x_test_linear)\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.scatter(x_train_outliers[:, 0], x_train_outliers[:, 1], c=t_outliers)\n",
    "plt.contourf(x1, x2, predicted_outliers.reshape(100, 100), alpha=0.2, levels=np.linspace(0, 1, 3))\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(-5, 5)\n",
    "plt.xlabel(\"$x_1$\", fontsize=12)\n",
    "plt.ylabel(\"$x_2$\", fontsize=12)\n",
    "plt.title(\"Outliers decision boundary\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3dd6c46f",
   "metadata": {},
   "source": [
    "The failure of least squares should not surprise us since it corresponds to maximum likelihood under the assumption of a Gaussian conditional distribution, whereas binary target vectors clearly do not have a Gaussian distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1648744",
   "metadata": {},
   "source": [
    "### 4.1.4 Fisher's linear discriminant\n",
    "\n",
    "Consider a two-class problem in which there are $N_1$ points of class $\\mathcal{C}_1$ and $N_2$ points from class $\\mathcal{C}_2$, so that the mean vectors of the two classes are given by\n",
    "\n",
    "$$\n",
    "\\mathbf{m}_1 = \\frac{1}{N_1}\\sum_{n\\in\\mathcal{C}_1}\\mathbf{x}_n, \\qquad\\qquad \\mathbf{m}_2 = \\frac{1}{N_2}\\sum_{n\\in\\mathcal{C}_2}\\mathbf{x}_n\n",
    "$$\n",
    "\n",
    "Then, the simplest measure of separation of the classes, when projected onto $\\mathbf{w}$, is the separation of the projected class means. This suggests that we might choose $\\mathbf{w}$ so as to maximize \n",
    "\n",
    "$$\n",
    "m_2 - m_1 = \\mathbf{w}^T(\\mathbf{m}_2 - \\mathbf{m}_1)\n",
    "$$\n",
    "\n",
    "where\n",
    "\n",
    "$$\n",
    "m_k = \\mathbf{w}^T\\mathbf{m}_k\n",
    "$$\n",
    "\n",
    "is the mean of the projected data from class $\\mathcal{C}_k$.\n",
    "\n",
    "The idea proposed by Fisher is to maximize the function that gives a large separation between the projected class means while also giving a small variance within each class, thereby minimizing the class overlap. The within-class variance of the projected data from class $\\mathcal{C}_k$ is given by,\n",
    "\n",
    "$$\n",
    "s_k^2 = \\sum_{n\\in\\mathcal{C}_k} (y_n - m_k)^2\n",
    "$$\n",
    "\n",
    "where $y_n = \\mathbf{w}^T\\mathbf{x}_n$ is the projected data point in the one-dimentional space. We can further define the total within-class variance for the whole data set to be simply $s_1^2 + s_2^2$. Then, the Fisher criterion is defined as the ratio of the *between-class* variance to the *within-class* variance as follows,\n",
    "\n",
    "$$\n",
    "J(\\mathbf{w}) = \\frac{(m_2-m_1)^2}{s_1^2+s_2^2}\n",
    "$$\n",
    "\n",
    "In order to explicitly show the dependence on $\\mathbf{w}$, we may rewrite $J(\\mathbf{w})$, using $(4.20)$, $(4.23)$, and $(4.24)$, as follows,\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "J(\\mathbf{w}) &= \\frac{(m_2-m_1)^2}{s_1^2+s_2^2}\\\\\n",
    "&= \\frac{(\\mathbf{w}^T\\mathbf{m}_2-\\mathbf{w}^T\\mathbf{m}_1)^2}{\\sum_{n\\in\\mathcal{C}_k} (y_n - m_1)^2 + \\sum_{n\\in\\mathcal{C}_k} (y_n - m_2)^2}\\\\\n",
    "&= \\frac{(\\mathbf{w}^T(\\mathbf{m}_2-\\mathbf{m}_1))^2}{\\sum_{n\\in\\mathcal{C}_k} (\\mathbf{w}^T(\\mathbf{x}_n - \\mathbf{m}_1))^2 + \\sum_{n\\in\\mathcal{C}_k} (\\mathbf{w}^T(\\mathbf{x}_n - \\mathbf{m}_2))^2}\\\\\n",
    "&= \\frac{\\mathbf{w}^T(\\mathbf{m}_2-\\mathbf{m}_1)^2\\mathbf{w}}{\\mathbf{w}^T\\big(\\sum_{n\\in\\mathcal{C}_k} (\\mathbf{x}_n - \\mathbf{m}_1)^2 + \\sum_{n\\in\\mathcal{C}_k} (\\mathbf{x}_n - \\mathbf{m}_2)^2\\big)\\mathbf{w}}\\\\\n",
    "&=\\frac{\\mathbf{w}^T\\mathbf{S}_B\\mathbf{w}}{\\mathbf{w}^T\\mathbf{S}_W\\mathbf{w}}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Then, by computing the derivative with respect to $\\mathbf{w}$, we find that $J(\\mathbf{w})$ is maximized when,\n",
    "\n",
    "$$\n",
    "(\\mathbf{w}^T\\mathbf{S}_B\\mathbf{w})\\mathbf{S}_W\\mathbf{w} = (\\mathbf{w}^T\\mathbf{S}_W\\mathbf{w})\\mathbf{S}_B\\mathbf{w} \\Leftrightarrow \\mathbf{w} \\propto \\mathbf{S}_W^{-1}(\\mathbf{m}_2-\\mathbf{m}_1)\n",
    "$$\n",
    "\n",
    "This result is known as the *Fisher's linear discriminant*. To that end, the projected data are compared against a threshold $y_0$ and classified as belonging to class $\\mathcal{C}_1$ if $y(\\mathbf{x}) \\geq y_0$, and to class $\\mathcal{C}_2$ otherwise."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "eccc8b3a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 263,
       "width": 370
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# number of training points\n",
    "N = 100\n",
    "\n",
    "x_train, t = make_classification(\n",
    "    n_features=2, n_informative=2, n_redundant=0, n_classes=2, n_clusters_per_class=1, n_samples=N, random_state=15\n",
    ")\n",
    "\n",
    "x1, x2 = np.meshgrid(np.linspace(-5, 5, N), np.linspace(-5, 5, N))\n",
    "x_test = np.array([x1, x2]).reshape(2, -1).T\n",
    "\n",
    "plt.scatter(x_train[:, 0], x_train[:, 1], c=t)\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(-5, 5)\n",
    "plt.title(\"Training data (2 classes)\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "778439cc",
   "metadata": {},
   "source": [
    "One way of choosing the threshold $y_0$ is to model the class-conditional densities (one per class) $p(y|\\mathcal{C}_k)$ as Gaussian distributions, then estimate their parameters using maximum likelihood, and finally, estimate the optimal threshold using decision theory. In the case of binary classification, we can equate the Gaussian functions and solve for $\\mathbf{x}$. The result is a quadratic equation having coefficients relating to the gaussian means and variances."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "4b512547",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 263,
       "width": 372
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# split data points according to the classes\n",
    "x_0 = x_train[t == 0]\n",
    "x_1 = x_train[t == 1]\n",
    "\n",
    "model = FisherLinearDiscriminant()\n",
    "model.fit(x_train, t)\n",
    "\n",
    "# create a Gaussian distribution per class\n",
    "g0 = Gaussian()\n",
    "g0.ml(x_0 @ model._w)\n",
    "g1 = Gaussian()\n",
    "g1.ml(x_1 @ model._w)\n",
    "\n",
    "root = np.roots(\n",
    "    [\n",
    "        g1.var - g0.var,\n",
    "        2 * (g0.var * g1.mu - g1.var * g0.mu),\n",
    "        g1.var * g0.mu**2 - g0.var * g1.mu**2 - g1.var * g0.var * np.log(g1.var / g0.var),\n",
    "    ]\n",
    ")\n",
    "\n",
    "x = np.linspace(-5, 5, N)\n",
    "plt.plot(x, g0.pdf(x), \"springgreen\")\n",
    "plt.plot(x, g1.pdf(x), \"firebrick\")\n",
    "plt.plot(root[0], g0.pdf(root[0]), \"ko\")\n",
    "plt.plot(root[1], g0.pdf(root[1]), \"ko\")\n",
    "plt.plot(np.zeros(x.size) + root[1], np.linspace(0, 1, N), \"k--\")\n",
    "plt.title(\"Intersection point of Gaussian curves\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0959caba",
   "metadata": {},
   "source": [
    "The figures below compares the optimal threshold against the naive zero threshold. Note that the selection of the decision threshold is crucial for an effective model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "da186854",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 318,
       "width": 873
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = FisherLinearDiscriminant()\n",
    "model.fit(x_train, t)\n",
    "optimal_threshold = model._threshold\n",
    "\n",
    "plt.figure(figsize=(15, 5))\n",
    "\n",
    "# predict classes using the optimal threshold\n",
    "predicted = model.predict(x_test)\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.scatter(x_train[:, 0], x_train[:, 1], c=t)\n",
    "plt.contourf(x1, x2, predicted.reshape(N, N), alpha=0.2, levels=np.linspace(0, 1, 3))\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(-5, 5)\n",
    "plt.title(f\"Optimal threshold ({round(optimal_threshold, 2)})\")\n",
    "\n",
    "# set threshold to zero and make predictions\n",
    "model._threshold = 0\n",
    "predicted = model.predict(x_test)\n",
    "\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.scatter(x_train[:, 0], x_train[:, 1], c=t)\n",
    "plt.contourf(x1, x2, predicted.reshape(N, N), alpha=0.2, levels=np.linspace(0, 1, 3))\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(-5, 5)\n",
    "plt.title(\"Zero threshold (suboptimal)\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25e96427",
   "metadata": {},
   "source": [
    "### 4.1.7 The perceptron algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6530549f",
   "metadata": {},
   "source": [
    "Another linear discriminant model is the perceptron. It corresponds to a two-class model in which the input vector $\\mathbf{x}$ is first transformed using a nonlinear transformation to give a feature vector $\\boldsymbol\\phi(\\mathbf{x})$, and then use it to construct a generalized linear model of the form\n",
    "\n",
    "$$\n",
    "y(\\mathbf{x}) = f\\big(\\mathbf{w}^T\\boldsymbol\\phi(\\mathbf{x})\\big)\n",
    "$$\n",
    "\n",
    "We assume that the vector $\\boldsymbol\\phi(\\mathbf{x})$ typically includes the bias component $\\phi_0$. The nonlinear activation function $f(\\cdot)$ is given by a step function of the form\n",
    "\n",
    "$$\n",
    "f(\\alpha)=\n",
    "\\begin{cases}\n",
    "    +1, & \\quad \\alpha \\geq 0\\\\\n",
    "    -1, & \\quad \\alpha < 0\n",
    "\\end{cases}\n",
    "$$\n",
    "\n",
    "That is because for the perceptron it is more convenient to use target values $t=+1$ for class $\\mathcal{C}_1$ and $t=-1$ for class $\\mathcal{C}_2$, instead of $t \\in \\{0,1\\}$. We consider an error function called the *perceptron criterion*. Note that we are seeking a weight vector $\\mathbf{w}$, such that the inputs $\\mathbf{x}_n$, belonging in class $\\mathcal{C}_1$, have $\\mathbf{w}^T\\boldsymbol\\phi(\\mathbf{x}_n) > 0$, whereas the ones belonging in class $\\mathcal{C}_2$, have $\\mathbf{w}^T\\boldsymbol\\phi(\\mathbf{x}_n) < 0$. Given the coding scheme $t \\in \\{-1, +1\\}$, it follows that all inputs must satisfy $\\mathbf{w}^T\\boldsymbol\\phi(\\mathbf{x}_n)t_n > 0$. Thus, the perceptron criterion tries to minimize the quantity $-\\mathbf{w}^T\\boldsymbol\\phi(\\mathbf{x}_n)t_n$, for all misclassified inputs. More formally,\n",
    "\n",
    "$$\n",
    "E_P(\\mathbf{w}) = -\\sum_{n\\in\\mathcal{M}} \\mathbf{w}^T\\boldsymbol\\phi(\\mathbf{x}_n)t_n\n",
    "$$\n",
    "\n",
    "where $\\mathcal{M}$ denotes the set of misclassified patterns.\n",
    "\n",
    "We apply the stochastic gradient descent algorithm to the error function. Thus, the change in the weight vector, according to gradient descent, is given by,\n",
    "\n",
    "$$\n",
    "\\mathbf{w}^{(\\tau+1)} = \\mathbf{w}^{(\\tau)} - \\eta\\nabla E_P(\\mathbf{w}) = \\mathbf{w}^{(\\tau)} + \\eta\\boldsymbol\\phi_nt_n\n",
    "$$\n",
    "\n",
    "The *perceptron convergence theorem* states that if there exists an exact solution (the data are linearly separable), the the perceptron algorithm is guaranteed to find the solution in a finite number of steps. On the other hand, if the data are not linearly separable the perceptron never converges. Moreover, note that the perceptron **does not provide probabilistic outputs, nor does it generalize to $K>2$ classes**.\n",
    "\n",
    "Another important limitation arises from the fact that it is based on linear combinations of fixed basis functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "603d828a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 318,
       "width": 873
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# number of training points\n",
    "N = 100\n",
    "\n",
    "x1, x2 = np.meshgrid(np.linspace(-5, 5, N), np.linspace(-5, 5, N))\n",
    "x_test = np.array([x1, x2]).reshape(2, -1).T\n",
    "\n",
    "model = Perceptron()\n",
    "\n",
    "plt.figure(figsize=(15, 5))\n",
    "\n",
    "x_train, t = make_classification(\n",
    "    n_features=2,\n",
    "    n_informative=2,\n",
    "    n_redundant=0,\n",
    "    n_classes=2,\n",
    "    n_clusters_per_class=1,\n",
    "    n_samples=N,\n",
    "    random_state=10,\n",
    "    class_sep=2,\n",
    ")\n",
    "\n",
    "model.fit(x_train, np.where(t == 0, -1, 1))\n",
    "predicted = model.predict(x_test)\n",
    "\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.scatter(x_train[:, 0], x_train[:, 1], c=t)\n",
    "plt.contourf(x1, x2, predicted.reshape(N, N), alpha=0.2, levels=np.linspace(0, 1, 3))\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(-5, 5)\n",
    "plt.title(\"Linearly separable data\")\n",
    "\n",
    "x_train, t = make_classification(\n",
    "    n_features=2,\n",
    "    n_informative=2,\n",
    "    n_redundant=0,\n",
    "    n_classes=2,\n",
    "    n_clusters_per_class=1,\n",
    "    n_samples=N,\n",
    "    random_state=14,\n",
    ")\n",
    "\n",
    "model.fit(x_train, np.where(t == 0, -1, 1))\n",
    "predicted = model.predict(x_test)\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.scatter(x_train[:, 0], x_train[:, 1], c=t)\n",
    "plt.contourf(x1, x2, predicted.reshape(N, N), alpha=0.2, levels=np.linspace(0, 1, 3))\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(-5, 5)\n",
    "plt.title(\"Non-linearly separable data\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d4e27e7c",
   "metadata": {},
   "source": [
    "## 4.2 Probabilistic Generative Models\n",
    "\n",
    "Models having linear decision boundaries arise from simple assumptions about the distribution of the data. A generative approach models the class-conditional densities $p(\\mathbf{x}|\\mathcal{C}_k)$, as well as the class priors $p(\\mathcal{C}_k)$, and use them to compute the posterior probability $p(\\mathcal{C}_k|\\mathbf{x})$ throught *Bayes theorem*. To that end, the posterior probability for class $\\mathcal{C}_1$, in a binary classification problem, is as follows,\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "p(\\mathcal{C}_1|\\mathbf{x}) &= \\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1)}{p(\\mathbf{x})} \\\\\n",
    "&= \\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1)}{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1) + p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)} \\\\\n",
    "&= \\frac{1}{1 + \\exp(-\\alpha)} = \\sigma(\\alpha)\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "where,\n",
    "\n",
    "$$\n",
    "\\alpha = \\ln\\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1)}{p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)}\n",
    "$$\n",
    "\n",
    "*Proof*\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\sigma(\\alpha) &= \\frac{1}{1 + \\exp(-\\alpha)} \\\\\n",
    "&= \\frac{1}{1 + \\frac{1}{\\exp(\\alpha)}} = \\frac{\\exp(\\alpha)}{1 + \\exp(\\alpha)} \\\\\n",
    "&= \\frac{\\exp\\big(\\ln\\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1)}{p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)}\\big)}{1 + \\exp\\big(\\ln\\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1)}{p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)}\\big)} \\\\\n",
    "&= \\frac{\\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1)}{p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)}}{1 + \\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1)}{p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)}}\n",
    "= \\frac{\\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1)}{p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)}}{\\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1) + p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)}{p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)}} \\\\\n",
    "&= \\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1)p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)}{p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)\\big(p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1) + p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)\\big)} \\\\\n",
    "&= \\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1)}{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1) + p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "The function $\\sigma(\\alpha)$ is the **logistic sigmoid** briefly presented in [Chapter 3](ch3_linear_models_for_regression.ipynb).\n",
    "\n",
    "For $K>2$ classes, the posterior for class $\\mathcal{C}_k$ is as follows,\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "p(\\mathcal{C}_k|\\mathbf{x}) &= \\frac{p(\\mathbf{x}|\\mathcal{C}_k)p(\\mathcal{C}_k)}{p(\\mathbf{x})} \\\\\n",
    "&= \\frac{p(\\mathbf{x}|\\mathcal{C}_k)p(\\mathcal{C}_k)}{\\sum_i p(\\mathbf{x}|\\mathcal{C}_i)} \\\\\n",
    "&= \\frac{\\exp(\\alpha_k)}{\\sum_i \\exp(\\alpha_i)}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "which is known as the *normalized exponential* and can be regarded as a multiclass generalization of the logistic sigmoid function. The quantities $\\alpha_k$ are defined as follows,\n",
    "\n",
    "$$\n",
    "\\alpha_k = \\ln(p(\\mathbf{x}|\\mathcal{C}_k)p(\\mathcal{C}_k))\n",
    "$$\n",
    "\n",
    "The normalized exponential is also known as the *softmax function*, since it represents a smoothed version of the max function, because if $\\alpha_k \\gg \\alpha_i\\; \\forall i \\neq k$, then $p(\\mathcal{C}_k|\\mathbf{x}) \\approx 1$ and $p(\\mathcal{C}_i|\\mathbf{x}) \\approx 0$.\n",
    "\n",
    "### 4.2.1 Continuous inputs\n",
    "\n",
    "Given the formulation above, the next step is to assume the form of the class-conditional densities. The Gaussian distributions may be used for modelling continuous variables. Assuming that all classes share the same covariance matrix, the density for class $\\mathcal{C}_k$ is given by\n",
    "\n",
    "$$\n",
    "p(\\mathbf{x}|\\mathcal{C}_k) = \\mathcal{N}(\\mathbf{x}|\\boldsymbol\\mu_k, \\Sigma)\n",
    "$$\n",
    "\n",
    "Thus, from $(4.58)$, we have,\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\alpha &= \\ln\\frac{p(\\mathbf{x}|\\mathcal{C}_1)p(\\mathcal{C}_1)}{p(\\mathbf{x}|\\mathcal{C}_2)p(\\mathcal{C}_2)}\n",
    "= \\ln\\frac{\\mathcal{N}(\\mathbf{x}|\\boldsymbol\\mu_1, \\Sigma)p(\\mathcal{C}_1)}{\\mathcal{N}(\\mathbf{x}|\\boldsymbol\\mu_2, \\Sigma)p(\\mathcal{C}_2)} \\\\\n",
    "&= \\ln\\frac{\\mathcal{N}(\\mathbf{x}|\\boldsymbol\\mu_1, \\Sigma)}{\\mathcal{N}(\\mathbf{x}|\\boldsymbol\\mu_2, \\Sigma)}\n",
    "+ \\ln\\frac{p(\\mathcal{C}_1)}{p(\\mathcal{C}_2)} \\\\\n",
    "&= \\ln\\frac{\\exp\\big\\{-\\frac{1}{2}(\\mathbf{x}-\\boldsymbol\\mu_1)^T\\Sigma^{-1}(\\mathbf{x}-\\boldsymbol\\mu_1)\\big\\}}{\\exp\\big\\{-\\frac{1}{2}(\\mathbf{x}-\\boldsymbol\\mu_2)^T\\Sigma^{-1}(\\mathbf{x}-\\boldsymbol\\mu_2)\\big\\}}\n",
    "+ \\ln\\frac{p(\\mathcal{C}_1)}{p(\\mathcal{C}_2)} \\\\\n",
    "&= -\\frac{1}{2}(\\mathbf{x}-\\boldsymbol\\mu_1)^T\\Sigma^{-1}(\\mathbf{x}-\\boldsymbol\\mu_1) + \\frac{1}{2}(\\mathbf{x}-\\boldsymbol\\mu_2)^T\\Sigma^{-1}(\\mathbf{x}-\\boldsymbol\\mu_2) + \\ln\\frac{p(\\mathcal{C}_1)}{p(\\mathcal{C}_2)} \\\\\n",
    "&= - \\frac{1}{2}\\mathbf{x}^T\\Sigma^{-1}\\mathbf{x} + \\boldsymbol\\mu_1^T\\Sigma^{-1}\\mathbf{x} - \\frac{1}{2}\\boldsymbol\\mu_1^T\\Sigma^{-1}\\boldsymbol\\mu_1\n",
    "+ \\frac{1}{2}\\mathbf{x}^T\\Sigma^{-1}\\mathbf{x} - \\boldsymbol\\mu_2^T\\Sigma^{-1}\\mathbf{x} + \\frac{1}{2}\\boldsymbol\\mu_2^T\\Sigma^{-1}\\boldsymbol\\mu_2 + \\ln\\frac{p(\\mathcal{C}_1)}{p(\\mathcal{C}_2)} \\\\\n",
    "&= \\boldsymbol\\mu_1^T\\Sigma^{-1}\\mathbf{x} - \\boldsymbol\\mu_2^T\\Sigma^{-1}\\mathbf{x} - \\frac{1}{2}\\boldsymbol\\mu_1^T\\Sigma^{-1}\\boldsymbol\\mu_1 + \\frac{1}{2}\\boldsymbol\\mu_2^T\\Sigma^{-1}\\boldsymbol\\mu_2 + \\ln\\frac{p(\\mathcal{C}_1)}{p(\\mathcal{C}_2)} \\\\\n",
    "&= (\\boldsymbol\\mu_1 - \\boldsymbol\\mu_2)^T\\Sigma^{-1}\\mathbf{x} - \\frac{1}{2}\\boldsymbol\\mu_1^T\\Sigma^{-1}\\boldsymbol\\mu_1 + \\frac{1}{2}\\boldsymbol\\mu_2^T\\Sigma^{-1}\\boldsymbol\\mu_2 + \\ln\\frac{p(\\mathcal{C}_1)}{p(\\mathcal{C}_2)}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "To that end, using $(4.57)$, we derive that,\n",
    "\n",
    "$$\n",
    "p(\\mathcal{C}_1|\\mathbf{x}) = \\sigma(\\mathbf{w}^T\\mathbf{x} + w_0)\n",
    "$$\n",
    "\n",
    "where,\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\mathbf{w} &= \\Sigma^{-1}(\\boldsymbol\\mu_1-\\boldsymbol\\mu_2) \\\\\n",
    "w_0 &= -\\frac{1}{2}\\boldsymbol\\mu_1^T\\Sigma^{-1}\\boldsymbol\\mu_1 + \\frac{1}{2}\\boldsymbol\\mu_2^T\\Sigma^{-1}\\boldsymbol\\mu_2 + \\ln\\frac{p(\\mathcal{C}_1)}{p(\\mathcal{C}_2)}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Note that the prior probabilities $p(\\mathcal{C}_k)$ enter through the bias parameter $w_0$, thus making parallel shifts of the decision boundary.\n",
    "\n",
    "For the general case of $K$ classes, from $(4.63)$, we have, \n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\alpha_k &= \\ln\\Big(\\frac{1}{(2\\pi)^{D/2}}\\Big) + \\ln\\Big(\\frac{1}{|\\Sigma|^{1/2}}\\Big) -\\frac{1}{2}(\\mathbf{x}-\\boldsymbol\\mu_k)^T\\Sigma^{-1}(\\mathbf{x}-\\boldsymbol\\mu_k) + \\ln p(\\mathcal{C}_k) \\\\\n",
    "&= \\ln\\Big(\\frac{1}{(2\\pi)^{D/2}}\\Big) + \\ln\\Big(\\frac{1}{|\\Sigma|^{1/2}}\\Big) - \\frac{1}{2}\\mathbf{x}^T\\Sigma^{-1}\\mathbf{x} + \\boldsymbol\\mu_k^T\\Sigma^{-1}\\mathbf{x} - \\frac{1}{2}\\boldsymbol\\mu_k^T\\Sigma^{-1}\\boldsymbol\\mu_k + \\ln p(\\mathcal{C}_k) \\\\\n",
    "&= \\ln A + \\ln B + Q + \\mathbf{w}_k^T\\mathbf{x} + w_{k0}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "where,\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "A &= \\ln\\Big(\\frac{1}{(2\\pi)^{D/2}}\\Big) \\\\\n",
    "B &= \\ln\\Big(\\frac{1}{|\\Sigma|^{1/2}}\\Big) \\\\\n",
    "Q &= - \\frac{1}{2}\\mathbf{x}^T\\Sigma^{-1}\\mathbf{x} \\\\\n",
    "\\mathbf{w}_k &= \\Sigma^{-1}\\mu_k \\\\\n",
    "\\mathbf{w}_{k0} &= - \\frac{1}{2}\\boldsymbol\\mu_k^T\\Sigma^{-1}\\boldsymbol\\mu_k + \\ln p(\\mathcal{C}_k)\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Then using $(4.62)$, we derive,\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "p(\\mathcal{C}_k|\\mathbf{x}) &= \\frac{\\exp(\\alpha_k)}{\\sum_j \\exp(\\alpha_j)} \\\\\n",
    "&= \\frac{\\exp(A + B + Q)\\exp(\\mathbf{w}_k^T\\mathbf{x} + w_{k0})}{\\exp(A + B + Q) \\sum_j \\exp(\\mathbf{w}_j^T\\mathbf{x} + w_{j0})}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "and re-define $\\alpha_k$ as follows,\n",
    "\n",
    "$$\n",
    "a_k(\\mathbf{x}) = \\mathbf{w}_k^T\\mathbf{x} + w_{k0}\n",
    "$$\n",
    "\n",
    "Therefore, we see that for $K>2$ classes, $\\alpha_k$ are linear functions of $\\mathbf{x}$ since quadratic terms cancel each other due to the shared covariances. By relaxing the assumption of the shared covariance matrix among the classes, allowing each class to have each won covariance matrix $\\Sigma_k$, then we obtain quadratic functions of $\\mathbf{x}$, giving rise to *quadratic discriminant*.\n",
    "\n",
    "### 4.2.2 Maximum likelihood solution\n",
    "\n",
    "Given a set of data, comprising observations $\\mathbf{x}$ and corresponding class labels, we can determine the parameters of the class-conditional densities and class prior probabilities, using maximum likelihood. Suppose that we are given a dataset $\\{\\mathbf{x},t_n\\}$, where $t_n=1$ denotes class $\\mathcal{C}_1$ and $t_n=0$ denotes $\\mathcal{C}_2$. Then, for a data point $\\mathbf{x}_n$ belonging to class $\\mathcal{C}_1$ ($t_n=1$), we have,\n",
    "\n",
    "$$\n",
    "p(\\mathbf{x}_n,\\mathcal{C}_1) = p(\\mathcal{C}_1)p(\\mathbf{x}_n|\\mathcal{C}_1) = \\pi\\mathcal{N}(\\mathbf{x}_n|\\boldsymbol\\mu_1, \\Sigma)\n",
    "$$\n",
    "\n",
    "Similarly, for class $\\mathcal{C}_2$ ($t_n=0$),\n",
    "\n",
    "$$\n",
    "p(\\mathbf{x}_n,\\mathcal{C}_2) = p(\\mathcal{C}_2)p(\\mathbf{x}_n|\\mathcal{C}_2) =(1-\\pi)\\mathcal{N}(\\mathbf{x}_n|\\boldsymbol\\mu_2, \\Sigma)\n",
    "$$\n",
    "\n",
    "where $p(\\mathcal{C}_1)=\\pi$ and complementary $p(\\mathcal{C}_2)=1-\\pi$.\n",
    "\n",
    "Thus, the likelihood function is given by,\n",
    "\n",
    "$$\n",
    "p(\\mathbf{t},\\mathbf{X}|\\pi,\\boldsymbol\\mu_1,\\boldsymbol\\mu_2,\\Sigma) = \\prod_{n=1}^N \\big[\\pi\\mathcal{N}(\\mathbf{x}_n|\\boldsymbol\\mu_1, \\Sigma)\\big]^{t_n} \\big[(1-\\pi)\\mathcal{N}(\\mathbf{x}_n|\\boldsymbol\\mu_2, \\Sigma)\\big]^{1-t_n}\n",
    "$$\n",
    "\n",
    "and the log-likelihood is as follows,\n",
    "\n",
    "$$\n",
    "\\ln p(\\mathbf{t},\\mathbf{X}|\\pi,\\boldsymbol\\mu_1,\\boldsymbol\\mu_2,\\Sigma) = \\sum_{n=1}^N t_n\\big(\\ln\\pi +\\ln\\mathcal{N}(\\mathbf{x}_n|\\boldsymbol\\mu_1, \\Sigma)\\big) + (1-t_n)\\big(\\ln(1-\\pi) + \\ln\\mathcal{N}(\\mathbf{x}_n|\\boldsymbol\\mu_2, \\Sigma)\\big)\n",
    "$$\n",
    "\n",
    "1. Setting the derivative for $\\pi$ equal to zero, we obtain,\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "&\\frac{d}{d\\pi} \\ln p(\\mathbf{t},\\mathbf{X}|\\pi,\\boldsymbol\\mu_1,\\boldsymbol\\mu_2,\\Sigma) = 0 \\Leftrightarrow \\\\ \n",
    "&\\frac{d}{d\\pi} \\sum_{n=1}^N\\{t_n\\ln\\pi + (1-t_n)\\ln(1-\\pi)\\} = 0 \\Leftrightarrow \\\\\n",
    "&\\frac{1}{\\pi}\\sum_{n=1}^N t_n - \\frac{1}{1-\\pi}\\sum_{n=1}^N(1-t_n) = 0 \\Leftrightarrow \\\\\n",
    "&\\frac{1}{\\pi}\\sum_{n=1}^N t_n - \\frac{1}{1-\\pi}(N-\\sum_{n=1}^N t_n) = 0 \\Leftrightarrow \\\\\n",
    "&\\frac{1}{\\pi}\\sum_{n=1}^N t_n = \\frac{1}{1-\\pi}(N-\\sum_{n=1}^N t_n) \\Leftrightarrow \\\\\n",
    "&\\frac{1-\\pi}{\\pi}\\sum_{n=1}^N t_n = N-\\sum_{n=1}^N t_n \\Leftrightarrow \\\\\n",
    "&\\frac{1}{\\pi}\\sum_{n=1}^N t_n - \\sum_{n=1}^N t_n = N-\\sum_{n=1}^N t_n \\Leftrightarrow \\\\\n",
    "&\\pi = \\frac{1}{N}\\sum_{n=1}^N t_n\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "As expected, the maximum likelihood estimate for $\\pi$, is simply the fraction of points in class $\\mathcal{C}_1$.\n",
    "\n",
    "2. Setting the derivative for $\\boldsymbol\\mu_1$ equal to zero, we obtain,\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "&\\frac{d}{d\\boldsymbol\\mu_1} \\ln p(\\mathbf{t},\\mathbf{X}|\\pi,\\boldsymbol\\mu_1,\\boldsymbol\\mu_2,\\Sigma) = 0 \n",
    "\\Leftrightarrow \\\\ \n",
    "&\\frac{d}{d\\boldsymbol\\mu_1} \\sum_{n=1}^N t_n\\ln\\mathcal{N}(\\mathbf{x}_n|\\boldsymbol\\mu_1, \\Sigma) = 0 \n",
    "\\Leftrightarrow \\\\\n",
    "&\\frac{d}{d\\boldsymbol\\mu_1} \\bigg[ -\\frac{1}{2}\\sum_{n=1}^N t_n(\\mathbf{x}_n-\\boldsymbol\\mu_1)^T\\Sigma^{-1}(\\mathbf{x}_n-\\boldsymbol\\mu_1) \\bigg] = 0 \\Leftrightarrow \\\\\n",
    "&-\\frac{1}{2}\\sum_{n=1}^N -2t_n\\Sigma^{-1}(\\mathbf{x}_n-\\boldsymbol\\mu_1) = 0 \\Leftrightarrow \\\\\n",
    "&\\sum_{n=1}^N t_n(\\mathbf{x}_n-\\boldsymbol\\mu_1) = 0 \\overset{\\sum_{n=1}^N t_n = N_1}{\\Leftrightarrow} \\\\\n",
    "&\\sum_{n=1}^N t_n\\mathbf{x}_n = N_1\\boldsymbol\\mu_1 \\Leftrightarrow \\\\\n",
    "&\\boldsymbol\\mu_1 = \\frac{1}{N_1}\\sum_{n=1}^N t_n\\mathbf{x}_n\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "3. Similarly, the corresponding result for $\\boldsymbol\\mu_2$ is given by,\n",
    "\n",
    "$$\n",
    "\\boldsymbol\\mu_2 = \\frac{1}{N_2}\\sum_{n=1}^N (t_n-1)\\mathbf{x}_n\n",
    "$$\n",
    "\n",
    "4. Finally, the solution for the shared covariance matrix $\\Sigma$ is similar to the one derived for the multivariate Gaussian distribution is [Chapter 2](ch2_probability_distributions.ipynb), where the matrix $\\Sigma$ is defined in $(4.78)$, $(4.79)$, and $(4.80)$.\n",
    "\n",
    "**Note**: Fitting Gaussian distributions to the classes is not robust to outliers, because the maximum likelihood estimation of a Gaussian is not robust itself.\n",
    "\n",
    "\n",
    "### 4.2.3 Discrete features\n",
    "\n",
    "Consider the case of discrete binary feature values $x_i \\in \\{0, 1\\}$. When there are $D$ inputs, then a general distribution would correspond to $2^D-1$ independent variables. Assuming a *naive Bayes* approach, we have the following class-conditional mass functions,\n",
    "\n",
    "$$\n",
    "p(\\mathbf{x}|\\mathcal{C}_k) = \\prod_{i=1}^D \\mu_{ki}^{x_i}(1-\\mu_{ki})^{1-x_i}\n",
    "$$\n",
    "\n",
    "For $K$ classes, substituting into $(4.63)$, gives,\n",
    "\n",
    "$$\n",
    "\\alpha_k(\\mathbf{x}) = \\sum_{i=1}^D \\big(x_i\\ln\\mu_{ki} + (1-x_i)\\ln(1-\\mu_{ki})\\big) + \\ln p(\\mathcal{C}_k)\n",
    "$$\n",
    "\n",
    "In the more general case, where discrete variables can take $M > 2$ states, the class-conditional mass functions are defined as follows,\n",
    "\n",
    "$$\n",
    "p(\\mathbf{x}|\\mathcal{C}_k) = \\prod_{i=1}^D\\prod_{m=1}^M \\mu_{kim}^{\\phi(x_i)_m}\n",
    "$$\n",
    "\n",
    "where $\\phi(x_i)$ produces a $1$-of-$M$ binary coding scheme, where only one of the value among $\\phi(x_i)_1,\\dots,\\phi(x_i)_M$ is $1$, and the others are all $0$. Thus, by substituting the expression above into $(4.63)$, gives,\n",
    "\n",
    "$$\n",
    "\\alpha_k(\\mathbf{x}) = \\sum_{i=1}^D\\sum_{m=1}^M \\big(\\phi(x_i)_m\\ln\\mu_{kim}\\big) + \\ln p(\\mathcal{C}_k)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "33772469",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 248,
       "width": 370
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# number of training points\n",
    "N = 100\n",
    "\n",
    "x_train, t = make_classification(\n",
    "    n_features=2, n_informative=2, n_redundant=0, n_classes=2, n_clusters_per_class=1, n_samples=N, random_state=21\n",
    ")\n",
    "\n",
    "x1, x2 = np.meshgrid(np.linspace(-5, 5, N), np.linspace(-5, 5, N))\n",
    "x_test = np.array([x1, x2]).reshape(2, -1).T\n",
    "\n",
    "model = GenerativeClassifier()\n",
    "model.fit(x_train, t)\n",
    "predicted = model.predict(np.array([np.ravel(x1), np.ravel(x2)]))\n",
    "\n",
    "plt.scatter(x_train[:, 0], x_train[:, 1], c=t)\n",
    "plt.contourf(x1, x2, predicted.reshape(N, N), alpha=0.2, levels=np.linspace(0, 1, 3))\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(-5, 5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8694285",
   "metadata": {},
   "source": [
    "## 4.3 Probabilistic Discriminative Models\n",
    "\n",
    "An alternative approach, called *discriminative training*, is to directly maximize the likelihood function defined through the conditional distribution $p(\\mathcal{C}_k|\\mathbf{x})$.\n",
    "\n",
    "### 4.3.2 Logistic Regression\n",
    "\n",
    "Consider the binary classification problem. In the analysis of generative approaches we saw that under rather general assumptions, the posterior probability of class $\\mathcal{C}_1$ can be expressed as a logistic sigmoid acting on a linear function of the input vectors $\\mathbf{x}$ or the feature vector $\\boldsymbol\\phi$ (see $4.65$) so that,\n",
    "\n",
    "$$\n",
    "p(\\mathcal{C}_1|\\boldsymbol\\phi) = y(\\boldsymbol\\phi) = \\sigma(\\mathbf{w}^T\\boldsymbol\\phi)\n",
    "$$\n",
    "\n",
    "In the terminology of statistics, this model is known as *logistic regression*, although its a classification model.\n",
    "\n",
    "> One advantage of the discriminative approach is that there are typically fewer adaptive parameters to be determined. For an $M$-dimensional feature space, this model has $M$ adjustable parameters. By contrast, the generative model using Gaussian class conditional densities, would have used $2M$ parameters for the means and $M(M+1)/2$ parameters for the (shared) covariance matrix.\n",
    "\n",
    "We can use maximum likelihood to determine the parameters of the logistic regression model. Given a data set $\\{\\boldsymbol\\phi_n, t_n\\}$, where $t_n\\in\\{0,1\\}$, the likelihood function is given by,\n",
    "\n",
    "$$\n",
    "p(\\mathbf{t}|\\boldsymbol{\\Phi},\\mathbf{w}) = \\prod_{n=1}^N p(\\mathcal{C}_1|\\boldsymbol\\phi_n)^{t_n}\\big(1-p(\\mathcal{C}_1|\\boldsymbol\\phi_n)\\big)^{1-t_n} = \\prod_{n=1}^N y_n^{t_n}\\{1-y_n\\}^{1-t_n}\n",
    "$$\n",
    "\n",
    "The maximum likelihood is equivalent to the minimum of the negative of the logarithm of the likelihood, which gives the *cross-entropy error function*,\n",
    "\n",
    "$$\n",
    "E(\\mathbf{w}) = -\\ln p(\\mathbf{t}|\\boldsymbol{\\Phi},\\mathbf{w}) = - \\sum_{n=1}^N t_n \\ln y_n + (1-t_n)\\ln(1-y_n)\n",
    "$$\n",
    "\n",
    "> **Why is the error function called cross-entropy?**\n",
    "> \n",
    "> The cross-entropy for discrete probability distributions $p$ and $q$ is defined as $H(p,q)=\\sum_{x} p(x)\\log q(x)$. Since we assume that the target variables $t_n$ are probabilities taking only extreme values $0$ or $1$, and $y_n$ is a probability distribution, then $E(\\mathbf{w})$ can be interpreted as the cross entropy of the target variables and the posterior probability distribution.\n",
    "\n",
    "Then, taking the gradient of the error function over $\\mathbf{w}$, we obtain,\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\nabla E(\\mathbf{w}) &= -\\nabla\\ln p(\\mathbf{t}|\\boldsymbol{\\Phi},\\mathbf{w}) \\\\\n",
    "&= -\\nabla \\sum_{n=1}^N t_n \\ln y_n + (1-t_n)\\ln(1-y_n) \\\\\n",
    "&= -\\sum_{n=1}^N \\frac{d}{dy_n}t_n \\ln y_n + \\frac{d}{dy_n}(1-t_n)\\ln(1-y_n) \\\\\n",
    "&\\overset{\\frac{d}{dx}\\ln f(x)=\\frac{f'(x)}{f(x)}}{=} -\\sum_{n=1}^N \\frac{d}{dy_n}t_n \\ln y_n + \\frac{d}{dy_n}(1-t_n)\\ln(1-y_n) \\\\\n",
    "&= -\\sum_{n=1}^N \\frac{t_n}{y_n}\\frac{d}{da_n}y_n\\frac{d}{d\\mathbf{w}}a_n - \\frac{1-t_n}{1-y_n}\\frac{d}{da_n}y_n\\frac{d}{d\\mathbf{w}}a_n \\\\\n",
    "&= -\\sum_{n=1}^N \\big(\\frac{t_n}{y_n} - \\frac{1-t_n}{1-y_n}\\big)\\frac{d}{da_n}y_n\\frac{d}{d\\mathbf{w}}a_n \\\\\n",
    "&= -\\sum_{n=1}^N \\big(\\frac{t_n}{y_n} - \\frac{1-t_n}{1-y_n}\\big)y_n(1-y_n)\\boldsymbol{\\phi}_n \\\\\n",
    "&\\overset{(4.88)}{=} -\\sum_{n=1}^N \\frac{t_n-y_n}{y_n(1-t_n)}y_n(1-y_n)\\boldsymbol{\\phi}_n \\\\\n",
    "&= \\sum_{n=1}^N (y_n - t_n)\\boldsymbol{\\phi}_n\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Note that the gradient takes the same form as the gradient of the sum-of-squares error function, however, $y_n$ involves a non-linear function. At this point we can make use of $(4.91)$ and $(3.22)$ to obtain a sequential algorithm (gradient descent) for optimizing the parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "482a2a0f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 334,
       "width": 889
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# number of training points\n",
    "N = 100\n",
    "\n",
    "# number of outlier points\n",
    "n_outliers = 5\n",
    "\n",
    "x_train, t = make_classification(\n",
    "    n_features=2, n_informative=2, n_redundant=0, n_classes=2, n_clusters_per_class=1, n_samples=N, random_state=12\n",
    ")\n",
    "\n",
    "x1, x2 = np.meshgrid(np.linspace(-5, 5, 100), np.linspace(-5, 5, 100))\n",
    "x_test = np.array([x1, x2]).reshape(2, -1).T\n",
    "\n",
    "outliers = np.random.random_sample((n_outliers, 2)) + 3\n",
    "x_train_outliers = np.vstack((x_train, outliers))\n",
    "t_outliers = np.hstack((t, np.ones(n_outliers, dtype=int)))\n",
    "\n",
    "feature = LinearFeature()\n",
    "x_train_linear = feature.transform(x_train)\n",
    "x_train_linear_outliers = feature.transform(x_train_outliers)\n",
    "x_test_linear = feature.transform(x_test)\n",
    "\n",
    "model = LogisticRegression()\n",
    "model.fit_lms(x_train_linear, t, 0.01)\n",
    "predicted = model.predict(x_test_linear)\n",
    "\n",
    "plt.figure(figsize=(15, 5))\n",
    "\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.scatter(x_train[:, 0], x_train[:, 1], c=t)\n",
    "plt.contourf(x1, x2, predicted.reshape(100, 100), alpha=0.2, levels=np.linspace(0, 1, 3))\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(-5, 5)\n",
    "plt.xlabel(\"$x_1$\", fontsize=12)\n",
    "plt.ylabel(\"$x_2$\", fontsize=12)\n",
    "plt.title(\"Original decision boundary\")\n",
    "\n",
    "model.fit_lms(x_train_linear_outliers, t_outliers, 0.01)\n",
    "predicted_outliers = model.predict(x_test_linear)\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.scatter(x_train_outliers[:, 0], x_train_outliers[:, 1], c=t_outliers)\n",
    "plt.contourf(x1, x2, predicted_outliers.reshape(100, 100), alpha=0.2, levels=np.linspace(0, 1, 3))\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(-5, 5)\n",
    "plt.xlabel(\"$x_1$\", fontsize=12)\n",
    "plt.ylabel(\"$x_2$\", fontsize=12)\n",
    "plt.title(\"Outliers decision boundary\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f4b21e3",
   "metadata": {},
   "source": [
    "Note that logistic regression is robust to outliers in contrast to linear discriminants presented in section [4.1](#4.1-Discriminant-Functions)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9b1a37d8",
   "metadata": {},
   "source": [
    "### 4.3.3 Iterative reweighted least squares\n",
    "\n",
    "In linear regression models, the maximum likelihood solution, on the assumption of Gaussian noise model, leads to a closed-form solution. For logistic regression, there is no longer a closed-form solution, due to the nonlinearity of the logistic sigmoid function. However, the error function is still convex and can be minimized by an efficient iterative technique based on *Newton-Raphson* iterative optimization scheme. This algorithm uses a local quadratic approximation to the log-likelihood, and takes the form\n",
    "\n",
    "$$\n",
    "\\mathbf{w}^{new} = \\mathbf{w}^{old} - \\mathbf{H}^{-1}\\nabla E(\\mathbf{w})\n",
    "$$\n",
    "\n",
    "where $\\mathbf{H}$ is the Hessian matrix whose elements comprise the second derivatives of $E(\\mathbf{w})$ over $\\mathbf{w}$.\n",
    "\n",
    "Note that, if we apply the *Newton-Raphson* algorithm to the linear regression model, we derive the standard least squares solution (see $4.94$ and $4.95$).\n",
    "\n",
    "Applying the *Newton-Raphson* update to the cross-entropy error function for the logistic regression model, we obtain,\n",
    "\n",
    "$$\n",
    "\\nabla E(\\mathbf{w}) = \\sum_{n=1}^N(y_n-t_n)\\boldsymbol\\phi_n = \\boldsymbol\\Phi^T(\\mathsf{y}-\\mathsf{t})\n",
    "$$\n",
    "\n",
    "and\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\mathbf{H} &= \\nabla\\nabla E(\\mathbf{w}) \\\\\n",
    "&= \\nabla\\sum_{n=1}^N(y_n-t_n)\\boldsymbol\\phi_n \\\\\n",
    "&= \\nabla\\sum_{n=1}^N y_n\\boldsymbol\\phi_n \\\\\n",
    "&\\overset{(4.88)}{=} \\sum_{n=1}^N y_n(1-y_n)\\boldsymbol\\phi_n\\frac{d}{d\\mathbf{w}}\\mathbf{w}^T\\boldsymbol\\phi_n \\\\ \n",
    "&= \\sum_{n=1}^N y_n(1-y_n)\\boldsymbol\\phi_n\\boldsymbol\\phi_n^T \\\\\n",
    "&= \\mathbf{\\Phi}^T\\mathbf{R}\\mathbf{\\Phi}\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "where $\\mathbf{R}$ is a diagonal matrix whose elements are $R_{nn}=y_n(1-y_n)$. Then, the update formula becomes,\n",
    "\n",
    "$$\n",
    "\\mathbf{w}^{new} = \\mathbf{w}^{old} - (\\mathbf{\\Phi}^T\\mathbf{R}\\mathbf{\\Phi})^{-1}\\boldsymbol\\Phi^T(\\mathsf{y}-\\mathsf{t})\n",
    "$$\n",
    "\n",
    "Note that Hessian depends on $\\mathbf{w}$ through the weighting matrix $\\mathbf{R}$, corresponding to the fact that the error function is no longer quadratic. Thus, we must apply the update formula iteratively, each time using the new weight vector $\\mathbf{w}$ to compute the revised weighting matrix $\\mathbf{R}$. To that end, the algorithm is known as *iterative reweighted least squares* or *IRLS*.\n",
    "\n",
    "The elements of $\\mathbf{R}$ can be interpreted as variances, given by,\n",
    "\n",
    "$$\n",
    "\\mathbb{E}[t] = \\sum_{t\\in\\{0,1\\}} t p(t|\\mathbf{x}) = \\sigma(x)\n",
    "$$\n",
    "\n",
    "and\n",
    "\n",
    "$$\n",
    "\\text{var}[t] = \\mathbb{E}[t^2] - \\mathbb{E}[t]^2 \\overset{t^2 = t}{=} \\mathbb{E}[t] - \\mathbb{E}[t]^2 =\n",
    "\\sigma(x) - \\sigma(x)^2 = y(1-y)\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "7b0d5774",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 334,
       "width": 889
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# number of training points\n",
    "N = 100\n",
    "\n",
    "# number of outlier points\n",
    "n_outliers = 5\n",
    "\n",
    "x_train, t = make_classification(\n",
    "    n_features=2, n_informative=2, n_redundant=0, n_classes=2, n_clusters_per_class=1, n_samples=N, random_state=12\n",
    ")\n",
    "\n",
    "x1, x2 = np.meshgrid(np.linspace(-5, 5, 100), np.linspace(-5, 5, 100))\n",
    "x_test = np.array([x1, x2]).reshape(2, -1).T\n",
    "\n",
    "outliers = np.random.random_sample((n_outliers, 2)) + 3\n",
    "x_train_outliers = np.vstack((x_train, outliers))\n",
    "t_outliers = np.hstack((t, np.ones(n_outliers, dtype=int)))\n",
    "\n",
    "feature = LinearFeature()\n",
    "x_train_linear = feature.transform(x_train)\n",
    "x_train_linear_outliers = feature.transform(x_train_outliers)\n",
    "x_test_linear = feature.transform(x_test)\n",
    "\n",
    "model = LogisticRegression()\n",
    "model.fit(x_train_linear, t)\n",
    "predicted = model.predict(x_test_linear)\n",
    "\n",
    "plt.figure(figsize=(15, 5))\n",
    "\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.scatter(x_train[:, 0], x_train[:, 1], c=t)\n",
    "plt.contourf(x1, x2, predicted.reshape(100, 100), alpha=0.2, levels=np.linspace(0, 1, 3))\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(-5, 5)\n",
    "plt.xlabel(\"$x_1$\", fontsize=12)\n",
    "plt.ylabel(\"$x_2$\", fontsize=12)\n",
    "plt.title(\"Original decision boundary\")\n",
    "\n",
    "model.fit_lms(x_train_linear_outliers, t_outliers, 0.01)\n",
    "predicted_outliers = model.predict(x_test_linear)\n",
    "\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.scatter(x_train_outliers[:, 0], x_train_outliers[:, 1], c=t_outliers)\n",
    "plt.contourf(x1, x2, predicted_outliers.reshape(100, 100), alpha=0.2, levels=np.linspace(0, 1, 3))\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(-5, 5)\n",
    "plt.xlabel(\"$x_1$\", fontsize=12)\n",
    "plt.ylabel(\"$x_2$\", fontsize=12)\n",
    "plt.title(\"Outliers decision boundary\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8cffab22",
   "metadata": {},
   "source": [
    "### [Gradient Descent vs Newton-Raphson](https://www.youtube.com/watch?v=iwO0JPt59YQ)\n",
    "\n",
    "Newton-Raphson method requires to compute the Hessian (through solving a set of linear equations) and thus, the computational cost for each iteration is higher than that of gradient descent. However, it usually converges faster than gradient descent in the sense that the number of iterations required is much smaller."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85d7707d",
   "metadata": {},
   "source": [
    "### 4.3.4 Multiclass logistic regression\n",
    "\n",
    "We have seen that for $K>2$ classes, the posterior probabilities are given by a softmax transformation of linear functions of feature variables. Here, we consider the maximum likelihood to determine the parameters $\\mathbf{w}_k$ of the model directly. To that end, we need to calculate the derivatives of $y_k$ (see $4.104$) over the activation functions $\\alpha_j$ (see $4.68$ and $4.105$).\n",
    "\n",
    "In order to find the derivatives, we need to consider $k\\neq j$ and $k=j$.\n",
    "\n",
    "1. $k\\neq j$\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\frac{\\partial y_k}{\\partial\\alpha_k} \n",
    "&= \\frac{\\partial}{\\partial\\alpha_k} \\frac{\\exp(\\alpha_k)}{\\sum_j \\exp(\\alpha_j)} \\\\\n",
    "&= \\frac{-\\exp(\\alpha_k)\\exp(\\alpha_j)}{\\big(\\sum_j \\exp(\\alpha_j)\\big)^2} \\\\\n",
    "&= -\\frac{\\exp(\\alpha_k)}{\\sum_j \\exp(\\alpha_j)}\\frac{\\exp(\\alpha_j)}{\\sum_j \\exp(\\alpha_j)} \\\\\n",
    "&\\overset{4.104}{=} -y_k y_j\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "2. $k=j$\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\frac{\\partial y_k}{\\partial\\alpha_k} \n",
    "&= \\frac{\\partial}{\\partial\\alpha_k} \\frac{\\exp(\\alpha_k)}{\\sum_j \\exp(\\alpha_j)} \\\\\n",
    "&= \\frac{\\exp(\\alpha_k)\\sum_j \\exp(\\alpha_j) - \\exp(\\alpha_k)^2}{\\big(\\sum_j \\exp(\\alpha_j)\\big)^2} \\\\\n",
    "&= \\frac{\\exp(\\alpha_k)\\sum_j \\exp(\\alpha_j)}{\\big(\\sum_j \\exp(\\alpha_j)\\big)^2} - \\frac{\\exp(\\alpha_k)^2}{\\big(\\sum_j \\exp(\\alpha_j)\\big)^2}\\\\\n",
    "&= \\frac{\\exp(\\alpha_k)}{\\sum_j \\exp(\\alpha_j)} - \\bigg(\\frac{\\exp(\\alpha_k)}{\\sum_j \\exp(\\alpha_j)}\\bigg)^2\\\\\n",
    "&=  y_k - y_k^2 \\\\\n",
    "&= y_k(1-y_k)\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "where we have used the quotient rule $\\big(\\frac{f}{g}\\big)'=\\frac{f'g-fg'}{g^2}$.\n",
    "\n",
    "\n",
    "Combining $(1)$ and $(2)$, we obtain,\n",
    "\n",
    "$$\n",
    "\\frac{\\partial y_k}{\\partial\\alpha_k} = y_k(I_{kj}-y_j)\n",
    "$$\n",
    "\n",
    "where $I_{kj}$ are the elements of the identity matrix.\n",
    "\n",
    "Assuming a $1$-of-$K$ coding scheme in which the target vector $\\mathbf{t}_k$ is a binary vector having all elements zero except for element $k$, which equals to one, then ,the likelihood function is then given by,\n",
    "\n",
    "$$\n",
    "p(\\mathbf{T}|\\mathbf{w}_1,\\dots,\\mathbf{w}_k) = \n",
    "\\prod_{n=1}^N \\prod_{k=1}^K p(\\mathbf{C}_k|\\boldsymbol\\phi_n)^{t_{nk}} =\n",
    "\\prod_{n=1}^N \\prod_{k=1}^K y_k(\\boldsymbol\\phi_n)^{t_{nk}}\n",
    "$$\n",
    "\n",
    "where $\\mathbf{T}$ is a $N\\times K$ matrix of target variables with elements $t_{nk}$. Taking the negative logarithm the gives,\n",
    "\n",
    "$$\n",
    "E(\\mathbf{w}_1,\\dots,\\mathbf{w}_k) = -\\ln p(\\mathbf{T}|\\mathbf{w}_1,\\dots,\\mathbf{w}_k) = \n",
    "-\\sum_{n=1}^N \\sum_{k=1}^K t_{nk}\\ln y_k(\\boldsymbol\\phi_n)\n",
    "$$\n",
    "\n",
    "which is the *cross-entropy* error function for the multiclass problem.\n",
    "\n",
    "Taking the gradient of the error function over the parameter vector $\\mathbf{w}_j$, we obtain\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\nabla_{\\mathbf{w}_j} E(\\mathbf{w}_1,\\dots,\\mathbf{w}_K) \n",
    "&= - \\nabla_{\\mathbf{w}_j} \\sum_{n=1}^N \\sum_{k=1}^K t_{nk}\\ln y_k(\\boldsymbol\\phi_n) \\\\\n",
    "&= - \\sum_{n=1}^N \\sum_{k=1}^K t_{nk}\\frac{1}{y_{nk}}y_{nk}(I_{kj}-y_{nj})\\boldsymbol\\phi_n \\\\\n",
    "&= - \\sum_{n=1}^N \\sum_{k=1}^K t_{nk}(I_{kj}-y_{nj})\\boldsymbol\\phi_n \\\\\n",
    "&= \\sum_{n=1}^N \\sum_{k=1}^K t_{nk}y_{nj}\\boldsymbol\\phi_n - \\sum_{n=1}^N \\sum_{k=1}^K t_{nk}I_{kj}\\boldsymbol\\phi_n \\\\\n",
    "&= \\sum_{n=1}^N \\sum_{k=1}^K t_{nk}y_{nj}\\boldsymbol\\phi_n - \\sum_{n=1}^N t_{nj}\\boldsymbol\\phi_n \\\\\n",
    "&\\overset{\\sum_k t_{nk}=1}{=} \\sum_{n=1}^N y_{nj}\\boldsymbol\\phi_n - \\sum_{n=1}^N t_{nj}\\boldsymbol\\phi_n \\\\\n",
    "&= \\sum_{n=1}^N (y_{nj} - t_{nj})\\boldsymbol\\phi_n\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "The Newton-Raphson update formula, requires the evaluation of the Hessian matrix, given by\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\nabla_{\\mathbf{w}_k} \\nabla_{\\mathbf{w}_j} E(\\mathbf{w}_1,\\dots,\\mathbf{w}_K) \n",
    "&= - \\nabla_{\\mathbf{w}_k} \\nabla_{\\mathbf{w}_j} \\ln p(\\mathbf{T}|\\mathbf{w}_1,\\dots,\\mathbf{w}_k) \\\\\n",
    "&= - \\nabla_{\\mathbf{w}_k} \\sum_{n=1}^N (y_{nj} - t_{nj})\\boldsymbol\\phi_n \\\\\n",
    "&= - \\nabla_{\\mathbf{w}_k} \\sum_{n=1}^N y_{nj}\\boldsymbol\\phi_n \\\\\n",
    "&= \\sum_{n=1}^N \\frac{\\partial}{\\partial\\mathbf{w}_k}y_{nj}\\boldsymbol\\phi_n \\\\\n",
    "&= \\sum_{n=1}^N y_{nk}(I_{kj}-y_{nj})\\boldsymbol\\phi_n\\boldsymbol\\phi_n^T \\\\\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "Below we present a softmax regression example trained using gradient descent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "ba3b77ec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 264,
       "width": 386
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# number of training points\n",
    "N = 100\n",
    "\n",
    "x_train, t = make_classification(\n",
    "    n_features=2, n_informative=2, n_redundant=0, n_classes=3, n_clusters_per_class=1, n_samples=N, random_state=21\n",
    ")\n",
    "\n",
    "x1, x2 = np.meshgrid(np.linspace(-5, 5, 100), np.linspace(-5, 5, 100))\n",
    "x_test = np.array([x1, x2]).reshape(2, -1).T\n",
    "\n",
    "model = SoftmaxRegression()\n",
    "model.fit(x_train, t)\n",
    "predicted = model.predict(x_test)\n",
    "\n",
    "plt.scatter(x_train[:, 0], x_train[:, 1], c=t)\n",
    "plt.contourf(x1, x2, predicted.reshape(100, 100), alpha=0.2, levels=np.linspace(0, 2, 4))\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(-5, 5)\n",
    "plt.xlabel(\"$x_1$\", fontsize=12)\n",
    "plt.ylabel(\"$x_2$\", fontsize=12)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6676eb8",
   "metadata": {},
   "source": [
    "## 4.4 Laplace Approximation\n",
    "\n",
    "In contrast to the [Bayesian treatment of linear regression](ch3_linear_models_for_regression.ipynb#3.3-Bayesian-Linear-Regression), in the Bayesian treatment of logistic regression, we cannot integrate exactly over the parameter vector $\\mathbf{w}$ since the posterior distribution is no longer Gaussian. To that end, we may use a widely used framework called the Laplace approximation, that aims to find a Gaussian approximation to a probability density defined over a set of continuous variables. Consider a single continuous variable $z$, having a distribution $p(z)$ defined by\n",
    "\n",
    "$$\n",
    "p(z) = \\frac{1}{Z}f(z)\n",
    "$$\n",
    "\n",
    "where $Z=\\int f(z)\\text{d}z$ is the normalization coefficient. The goal is to find a Gaussian approximation $q(z)$ centered on a mode of the distribution $p(z)$. The first step is to find a mode of $p(z)$, that is, a point $z_0$ such that $p'(z_0)=0$ or equivalently\n",
    "\n",
    "$$\n",
    "\\frac{df(z)}{dz}\\bigg|_{z=z_0} = 0\n",
    "$$\n",
    "\n",
    "Then, we use a second-order Taylor expansion to approximate $g(z) = \\ln f(z)$ (because the logarithm of any Gaussian distribution is a quadratic function of the variables), centered on the mode $z_0$ so that,\n",
    "\n",
    "$$\n",
    "g(z) = \\ln f(z) \\approx \\sum_{n=0}^{2} \\frac{g^{(n)}(z_0)}{n!}(z-z_0)^n = g(z_0) - \\frac{1}{2}g''(z_0)(z-z_0)^2\n",
    "$$\n",
    "\n",
    "Note that the first-order term is omitted since $z_0$ is a local maximum of the distribution and thus the derivative is zero. Then, taking the exponential on both sides of the expansion, we obtain\n",
    "\n",
    "$$\n",
    "f(z) \\approx f(z_0)\\exp\\Big\\{ -\\frac{A}{2}(z-z_0)^2 \\Big\\}\n",
    "$$\n",
    "\n",
    "where $A=-\\frac{d^2f(z)}{d^2z}$ on $z_0$. Therefore, using the standard result for the normalization of a Gaussian, the final normalized distribution $q(z)$ has the form,\n",
    "\n",
    "$$\n",
    "q(z) = \\Big(\\frac{A}{2\\pi}\\Big)^{1/2} \\exp\\Big\\{ -\\frac{A}{2}(z-z_0)^2 \\Big\\} = \\mathcal{N}(z|z_0,A)\n",
    "$$\n",
    "\n",
    "Note that the Gaussian approximation is well defined only when its precision $A>0$, which implies that $z_0$ must be a local maximum, not a minimum! In practice a mode may be found by running some form of numerical optimization. The Laplace approximation is depicted in the next Figure,\n",
    "\n",
    "<img src=\"../images/fg4_14a.png\" width=\"400\"/>\n",
    "\n",
    "The same approximation can be applied to an $M$-dimentional space $\\mathbf{z}$.\n",
    "\n",
    "## 4.5 Bayesian Logistic Regression\n",
    "\n",
    "Exact Bayesian inference for logistic regression, as well as, the evaluation of the predictive distribution are intractable. Thus, here, we consider the application of Laplace approximation for the problem of Bayesian logistic regression.\n",
    "\n",
    "### 4.5.1 Laplace approximation\n",
    "\n",
    "Similar to the Bayesian linear regression, we seek a Gaussian representation for the posterior distribution of the parameters, thus, we use a Gaussian (conjugate) prior in the general form,\n",
    "\n",
    "$$\n",
    "p(\\mathbf{w}) = \\mathcal{N}(\\mathbf{w}|\\mathbf{m}_0,\\mathbf{S}_0)\n",
    "$$\n",
    "\n",
    "where $\\mathbf{m}_0,\\mathbf{S}_0$ are fixed hyperparameters. Then, the posterior over $\\mathbf{w}$ is given by\n",
    "\n",
    "$$\n",
    "p(\\mathbf{w}|\\mathsf{t}) \\propto p(\\mathsf{t}|\\mathbf{w})p(\\mathbf{w})\n",
    "$$\n",
    "\n",
    "Taking the natural logarithm on both sides, and substituting for the prior and the likelihood, we obtain\n",
    "\n",
    "$$\n",
    "\\ln p(\\mathbf{w}|\\mathsf{t}) = \\ln\\Big(\\prod_{n=1}^N y_n^{t_n}\\{1-y_n\\}^{1-t_n}\\Big)\\ln \\mathcal{N}(\\mathbf{w}|\\mathbf{m}_0,\\mathbf{S}_0) = \\sum_{n=1}^N\\{t_n\\ln y_n + (1-t_n)\\ln(1-y_n)\\} + \\frac{1}{(2\\pi)^{D/2}|\\mathbf{S}_0|^{1/2}} -\\frac{1}{2}(\\mathbf{w}-\\mathbf{m}_0)^T\\mathbf{S}_0^{-1}(\\mathbf{w}-\\mathbf{m}_0)\n",
    "$$\n",
    "\n",
    "Then, to obtain the Gaussian approximation of the posterior, first, we maximize the posterior to give the MAP solution $\\mathbf{w}_{MAP}$, which corresponds to the mean of the approximated Gaussian. The covariance matrix is then given by the Hessian matrix of the negative log-likelihood,\n",
    "\n",
    "$$\n",
    "\\mathbf{S}_N^{-1} = -\\nabla\\nabla\\ln p(\\mathbf{w}|\\mathsf{t}) = \\mathbf{S}_0^{-1} + \\sum_{n=1}^N y_n(1-y_n)\\boldsymbol\\phi_n\\boldsymbol\\phi_n^T\n",
    "$$\n",
    "\n",
    "where we make use of $(4.97)$. Thus, the Gaussian approximation of the posterior takes the form,\n",
    "\n",
    "$$\n",
    "q(\\mathbf{w}) = \\mathcal{N}(\\mathbf{w}|\\mathbf{w}_{MAP},\\mathbf{S}_N)\n",
    "$$\n",
    "\n",
    "### 4.5.2 Predictive distribution\n",
    "\n",
    "The predictive distribution for class $\\mathcal{C}_1$, given a new feature vector $\\boldsymbol\\phi_{unseen}$, is obtained by marginalizing over the posterior distribution $p(\\mathbf{w}|\\mathsf{t})$, which is approximated by $q(\\mathbf{w})$, so that,\n",
    "\n",
    "$$\n",
    "p(\\mathcal{C}_1|\\boldsymbol\\phi_{unseen},\\mathsf{t},\\boldsymbol\\Phi) = \\int p(\\mathcal{C}_1|\\boldsymbol\\phi_{unseen},\\mathbf{w})p(\\mathbf{w}|\\mathsf{t},\\boldsymbol\\Phi)\\text{d}\\mathbf{w} \\approx \\int \\sigma(\\mathbf{w}^T\\boldsymbol\\phi)q(\\mathbf{w})\\text{d}\\mathbf{w}\n",
    "$$\n",
    "\n",
    "The evalution of the above integral is fairly complex and involves a significant number of steps. For more details see the corresponding section in the book. The final approximate predictive distribution has the form,\n",
    "\n",
    "$$\n",
    "p(\\mathcal{C}_1|\\boldsymbol\\phi_{unseen},\\mathsf{t}) = \\sigma\\big(\\kappa(\\sigma_{\\alpha}^2)\\mu_{\\alpha}\\big)\n",
    "$$\n",
    "\n",
    "where $\\kappa(\\sigma_{\\alpha}^2) = (1+ \\pi\\sigma_{\\alpha}^2/8)^{-1/2}$, $\\mu_a = \\mathbf{w}_{MAP}^T\\boldsymbol\\phi_{unseen}$, and $\\sigma_{\\alpha} = \\boldsymbol\\phi_{unseen}^T\\mathbf{S}_N\\boldsymbol\\phi_{unseen}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "14be25ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAtIAAAH4CAYAAABntQpnAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAABYlAAAWJQFJUiTwAAB4gklEQVR4nO3dd3hb1cHH8e+RZEue2TskISEhEEgIScggkxECNMykLW2ZLW2BlraUtm/L2wEdL10USmmZZRZoGWXvmQSSAIFAIGSTPcj2lG1J5/3j2omXbN1ryZLt3+d5/Mi+9yxjYv98fO45xlqLiIiIiIi440v3AERERERE2iIFaRERERERDxSkRUREREQ8UJAWEREREfFAQVpERERExAMFaRERERERDxSkRUREREQ8UJAWEREREfFAQVpERERExAMFaRERERERDxSkRUREREQ8UJAWEREREfFAQVpERERExAMFaRERERERDxSkRURERCTpjDFzjDE3G2PmG2OKjDHWGPOAx7b6G2P+aYzZaoypMMasN8bcaIzp0kSdI40x/zHGfG6MCRtjVhpjrjXG5Hj/rOr1Ya1NVlsiIiIiIgAYY5YCo4ASYDMwHPiXtfZrLtsZArwN9ASeBFYAxwEzgJXA8dba3fXqjAdeA7KAR4FNwAnAWOAt4ERrbYXXz62GZqRFREREJBV+AAwDCoHLWtDO33FC9JXW2rOstf9jrT0B+AtwOPDb2oWNMX7gbiAXmGOt/Yq19ifAeOAx4PjqsbWYZqRFREREJKWMMdOB13E5I109G70GWA8MsdbGat0rALYBBuhprS2tvn4C8Cowz1o7rV57g4G1wAbgUNvCIKwZaRERERHJVDOqX1+qHaIBrLXFOMs0coEJtW6dUP36Qv3GrLXrgFXAQGBwSwenIC0iIiIimerw6tdVce6vrn4d1sI6ngRa2kBbYIz5DGd9zvo0D0VERETaj0FAkbX20HQNwBjzL5yH+FJhEHGyk7V2TIr6rK9T9ev+OPdrrnduYR1POkSQBgpDoVDXIYOHdk33QERERKR9WLtuNeFwON3DGJ6TEzp22PAWr1KoY9WKdZSXh8uS2mg71FGC9Pohg4d2/e8jz6d7HCIiItJOnD33VD5Zvmx9uscxbPhgXl/4SFLbnDFxLh9+sHxFK848x1Mze9wpzv2a6/taWMcTrZEWERERkUy1svo13nrmodWvtddDe6njiYK0iIiIiGSq16tfZxpj6uTW6u3vjgfKgEW1br1W/TqrfmPV298Nw9n+bl1LB6cgLSIiIiJpZYzJMsYMr943+gBr7VrgJZwHH6+oV+1aIA+4v2YP6WpvAp8CU40xZ9Tqwwf8vvrDW1u6hzR0nDXSIiIiItKKjDFnAWdVf9i7+nWiMeae6vd3WWuvrn6/H0743YATmmu7HOeI8L8aY06sLjceZ4/pVcA1tQtba6PGmItxZqYfNcY8CmwETuTgEeF/afEniIK0iIiIiKTGMcCF9a4N5uBBKBuAq2mGtXatMWYscB3Oco3TcE40vAm41lq7t5E6i40x43BmrWcCBdX9XQdcb62t8PIJ1acgLSIiIiJJZ639FfCrBMuuxznqO979TcDFLvtfDsx1U8ctrZEWEREREfFAQVpERERExAMFaRERERERDxSkRUREREQ8UJAWEREREfFAQVpERERExAMFaRERERERDxSkRUREREQ8UJAWEREREfFAQVpERERExAMFaRERERERDxSkRUREREQ8UJAWEREREfFAQVpERERExAMFaRERERERDxSkRUREREQ8UJAWEREREfFAQVpERERExAMFaRERERERDxSkRUREREQ8UJAWEREREfFAQVpERERExAMFaRERERERDxSkRUREREQ8UJAWEREREfFAQVpERERExAMFaRERERERDxSkRUREREQ8UJAWEREREfEgY4O0MeZrxhhb/faNdI9HRERERKS2jAzSxphDgL8BJekei4iIiIhIYzIuSBtjDHA3sBu4Nc3DERERERFpVMYFaeBK4ATgYqA0zWMREREREWlURgVpY8wRwPXATdbaeekej4iIiIhIPIF0D6CGMSYA3A9sBH7msY0lcW4N9zouEREREZHGZEyQBn4BjAYmW2vL0z0YEREREZGmZESQNsaMx5mF/rO1dqHXdqy1Y+K0vwQ41mu7IiIiIiL1pX2NdPWSjvuAVcDP0zwcEREREZGEpD1IA/nAMOAIIFzrEBYL/LK6zB3V125M1yBFRERERGrLhKUdFcBdce4di7NuegGwEvC87ENEREREJJnSHqSrHyxs9AhwY8yvcIL0vdbaO1tzXCIiIiIiTcmEpR0iIiIiIm2OgrSIiIiIiAcZHaSttb+y1hot6xARERGRTJPRQVpEREREJFMpSIuIiIiIeJD2XTtERETamvKSMMvmf8q+z4vw+330HtyT4eOH4vcnf34qUhXhw9c/YdFz77Nv+z7wGXoO6M6kM4/jiPFD8flM0vsUkcQoSIuIiCSoeG8Jz972Coufe5+Ksoo697r16cK0L05ixnmT8QeSE6g/WbiKB659hP27iupc37JqGx+8soxeA7tzye++yiGH901KfyLijpZ2iIiIJGD31r384aJbmPfowgYhGmD3tr08ftOz3PGT+4lURVrc30fzPuUf37+7QYiubceGXdxw6a1sXLGlxf2JiHsK0iIiIs2oDFfxtyv/ye4te5ot+9Gby/nPH55qUX/Fe0u4+5oHiUVjzZatKKvgjh/dTzQSbVGfIuKegrSIiEgz3ntxKTvWf55w+beffIfd2/Z67u/tJ9+lorwy4fK7t+3lozeXe+5PRLxRkBYREWnGvEcXuiofi1kWPL7Yc39v/fdd13UW/Pcdz/2JiDcK0iIiIk0oLSpn46fu1yCvWLzaU39VFVXs2rLbdb3tn+3w1J+IeKcgLSIi0oRwSdhbvVJv9RJZF92YSJXWSIu0NgVpERGRJoTygp7qBXO91cvOyfbUZ+eenTz1JyLeKUiLiIg0Ibcwh37D+riud/i4oZ76M8Yw9pTRruuNm+W+joi0jIK0iIhIE4wxTJsz0XWdKeeM99zntLkTXJXPCgaY+IUxnvsTEW8UpEVERJox7tTR9OjfLeHyx51+LN37d/XcX7+hfTjxq1MSLn/uD2aT1znXc38i4o2CtIiISDOCOdlc/tdL6Nyr+XXIR0wYxld+enaL+zz7e6cz48uTmyxjjGHOVbOZOsfdDLaIJEcg3QMQERFpC3oN6M6P7/kOT/39RZa8tJSqirrHgHfqVsCUuRM55aLp+AP+Fvfn8xnmXj2bMTNHMu/RhSx5+SOi1TtzhPKCjD/tWKbMmUjfIb1a3JeIeKMgLSIikqDOPQq54JdzOfd7p7P09Y/Zt7MIf8BP70N7cPSUI5ISoOsbPHIgg0cO5LyfnUvJnhKMz1DQNZ+sbP0IF0k3/SsUERFxKa9zLseffVyr9hkMZRHs26VV+xSRpmmNtIiIiIiIBwrSIiIiIiIeKEiLiIiIiHigNdIiIpIS4dIKNny6mXBJBTn5IQaO6E8wJzvdwxIRSRoFaRERSarPN+3itX/NZ/FzH1BRVnHgek5+iAlfGMsJX51Mtz56aE5E2j4FaRERSZoV76zhth/dR0VpRYN75SVhXn94AYufW8JlN1zEkGMGtf4ARUSSSGukRUQkKTat3MqtV93baIiurayonL9//262r9/ZSiMTEUkNBWkREUmKp//xIpXhyoTKlpeEefaOV1I8IhGR1FKQFhGRFtu1ZQ+fvLXSVZ2lry5j/67iFI1IRCT1FKRFRKTFPpq3HGutqzrRSJRP3lqRohGJiKSegrSIiLRY6b4yb/X2e6snIpIJFKRFRKTFskNZnuplBb3VExHJBArSIiLSYgNHHOKp3iCP9UREMoGCtIiItNiwsUPoNbC7qzoDhvdj4Ij+KRqRiEjqKUiLiEiL+XyGk86f7qrOSedPwxiTmgGJiLQCnWwoIiJJMenMsWxetZU3//N2s2VPuWg6Y08Z1Qqj8sZay7oPN7DomSXs2roHY6B7325MPHMcg0b01y8AIgIoSIuISJIYY/jij86ge7+uvHjP65TsLW1QplO3Ak699ESmzpmYhhEmZvOqbdx37X/YvHJrvTtrWPDfxQw8sj8X/OqL9BncKy3jE5HMoSAtIiJJY4zhxK9OYerciXzw6jJWvbuGcFklobwgR0wYxjEzRuAP+NM9zLg2LN/MjZfd3uQx5xuWb+bPX/8HP7j9W/Qb2qcVRycimUZBWkREki4rO8Bxp47muFNHp3soCasIV3HrVfc2GaJrlBWXc+tV9/LLx68mkKUfpSIdlR42FBERAZa8uJT9u4oSLr97214+fP2TFI5IRDKdgrSIiAjw4t2vu64z77FFKRiJiLQVCtIiItLhxWKWnVt2u67X8IFEEelIFKRFRKTD27B8E1j39SorqpI/GBFpMxSkRUSkw9v46RZP9bKDWUkeiYi0JQrSIiLS4UUqIp7q9RrUM8kjEZG2RHv2iIhIhxCNxPh4wQoWPLGYbWu2E43E6NS9gLGzRpMV9PbjcPhxhyV5lCLSlihIi4hIu7dlzTZuv/p+dm6u+0Dh/l1FbFyxhUB2AJ/fRywac9XupDPHJXOYItLGKEiLiEi7tnXtDv5y6a2UFYfjlolUul/aMWLycLr369qSoYlIG6c10iIi0m5Za7n7mgebDNFeZIeyOPPyWUltU0TaHgVpERFpt1YtWceWNdtd1WluvXQoL8hlN15M/2F9WjI0EWkHtLRDRETarbefeMdDLcOJX5vK4meWULKv9MDVnPwQE74wlhnnHa8lHSICKEiLiEg79vnGXa7rVFVUMXXOBM64bCabVm6lvCRMKDdI/8P7EszJTsEoRaStUpAWEZF2KxbzcFwhEIvGyApmMXjkwCSPSKRjMcb0B64DZgHdgG3AE8C11tq9CdSfDryeQFcDrLWbatVr6h//YmvthATabJaCtIiItFtdenVi0wp3pxb6/D4KuxWkaEQiHYcxZgjwNtATeBJYARwHfA+YZYw53lq7u4kmANYD18a5dzRwDvBx7RBdywbgnkaub2528AlSkBYRkXZr/GnH8tGby13VGTVjBDn5oRSNSKRD+TtOiL7SWntzzUVjzA3AD4DfAt9uqgFr7XrgV43dM8Y8VP3uHXGqr7fWNlo3WbRrh4iItFsjp42gS69OrupMnTMxRaMR6TiqZ6Nn4swo31Lv9i+BUuB8Y0yex/a7A2cD5cB93kfaMgrSIiLSbvkDPs7/xVx8/sR+3E0+ZwLDxgxO8ahEOoQZ1a8vWWvrHBlqrS0G3gJyAa9rlS8EgsAj1tp9ccp0NsZcYoz5mTHmCmNMUtZF16alHSIi0q7t2rIHa5t/6HDKuRP44o/PxBjTCqMSaROGG2OWNHbDWjummbqHV7+uinN/Nc6M9TDgVQ9ju7T69bYmyowC7qp9wRjzIXC+tXaZhz4bUJAWEZF2a/FzH/Dg7x5PqGx5aRifTyFa2p6qmJ+tZZ2T3mYL1ayp2h/nfs31zm4bNsZMwwnqH1tr345T7AbgMZwgHwaGAz8B5gCvGWOOsda6exK5EQrSIiLSLlWEq3jkj08mXP69F5Yy8QtjOWLC0BSOSqRNWZHAzHM6fLP69fZ4Bay1P6x36T1grjHmUeBc4GqcBx5bRGukRUSkzdj3+X5WvreWTxetZuvaHU0u2XjvhaWUFZe7an/eY4taOkQRcdTMOMd72rfm+j43jRpjuuIE4XLgfg/jurX6daqHug1oRlpERDLeisWref3ht/h4wYo64bn/4X2ZNmciE2aPwR+o+6fo915a6rqfZW9+QkVZBcHcYEuHLNLRrax+HRbnfs2ffuKtoY6n5iHDe5t4yLApO6tfPe0WUp+CtIiIZCxrLU/9/UVevLvxg802r9zKv377GO+99CHf+tMFhPIOBuCiXcWu+4vFLMV7SxWkRVqu5h/tTGOMr/bOHcaYAuB4oAxw+2egmocM4y7raEbNzh3rPNavQ0s7REQkY71837y4Ibq2le+u4c7/eaDOkeC+gLcfcYGsFj9kJdLhWWvXAi8Bg4Ar6t2+FmdG+H5rbWnNRWPMcGPM8HhtGmOmAEfQ9EOGGGNGGmOyGruOcwgMwAMJfipN0oy0iIhkpNJ9ZTx7+0sJl1++cBWfvLWCo6ccAUC/w3qzZdU2V33md86joKuOBxdJkstxjgj/qzHmROBTYDzOHtOrgGvqlf+0+jXe9jnNPmRY7SpgtjFmPrAJqMDZtWMW4Mc5CfGh+NUTpxlpERHJSAufWUJVRcRVnXmPLDzw/uSzx7vuc9KZ4/B7nMkWkbqqZ6XHAvfgBOgfAkOAm4AJ1trdibZljOmCs3VdIg8ZPgG8CRyFs6b6SmAM8DxwprX2mzaRzeUToBlpERHJSEtfc39ewidvrzzwsOCQYwYxYHg/Nq5IbKtYf5afKecm/eAzaccqIu5+0euIrLWbgIsTLBt3I3dr7V4gJ8F2nsAJ0ymnIC0iIimze+teFvx3MZtXbqWqMkJBlzxGnziSUdOPbLDLRn0l+0qbvB+33v4ygrlBjDF84/qv8aev30LR7pIm6xhjuPBXX6Jb3y6e+pSOY+2uPekegmQQBWkREUm6suJyHvzt43zw6rIGez0vefkjOnUvZM4PZzPm5JFx28jK9vYjKit48Bmj7v27cvVdV/DP/32Q9R9varR8Ybd8zvvpuYyafqSn/qT9qx+eDzm0JwDZ2Q2eZ5MORkFaRESSqryknL9867YmH/Tbv6uIu376L8qLy5l8TuNrmQce2Z8ta7a76rtr787kd667PWz3/l350d1XsP6Tzbz1+CK2ffY50UiUTj0KOW7WaEbNGEEgSz8O5aB4wVmkPn3nEBGRpHrw/55IeLeMh6//LwOPPIRDhvdtcG/KuRN4+6n3XPU95dwJ+HwNl1kaYzj0qEM49KhDXLUnHYfCs3ihR5NFRCRp9mzfywcvf5hw+VjM8vq/32r03sARhzB0zOCE28otCDHprHEJlxdZu2vPgTdwwnPNm0giFKRFRCRp3n7ivTqHoiRiyUtLKSsub/Te7G/NpFOPTs22kRXM4pt/vJCCLvmu+paOR+FZkklLO0REJGk2rUpsq7naqioi7Niw68Cyi2gkxuLn3mfeI2+z8dPm2+t/eF++8tNzGKRlGxKHlm1IqmREkDbGdAPOBk4Hjgb6AZXAMuBu4O7aZ7SLiEhmilRGPdZz9uOtCFdx5/88wCcLVjRZvlu/Lhw58XDGn3Yshx49AGPibj8rHZCCs7SWjAjSwFzgH8A24HVgI9ALOAe4EzjVGDM3WafQiIhIahR287a0oqBrPtZa7v3Fw82GaIDdW/aSmx9i8MiBnvqT9kfhWdIhU4L0KuAM4NnaM8/GmJ8B7wDn4oTqx9IzPBGRtsFaS0VZJdGqKKH8UKsfd33sSSNZ/Oz7rur0G9qHXgO7s/r9z1j62scJ13v5vjeZOncSXXo1v4Za2ieFZ0m3jAjS1trX4lzfboy5FfgtMB0FaRGRRpXsK+XtJ99jweOL2bVlNwCBLD+jTzyaqXMmMnjUwFZZ/nDkpMPp1qcLu7ftTbjO8WcfhzGG+Y8udNVXLGZZ8N/FzP72zEbvh0sr2Pv5frCWTj0KyS1I6HRhyXAKz5JJMiJIN6Oq+lUH2ouINGLF4tXc/uP7CZdW1LkeqYry7gtLefeFpYz/whi+es05KT94xO/3MfdHZ3LbD+9tcKJhPG8/+Q6jpo/gwzc+cd3f0tc+bhCk13+8iTcfeZslL390YO21z+9j1PQjmTp3EsPGDNaa6jZEwVkyWUYHaWNMALig+sMXEii/JM6t4UkblIhIBlnzwWfc8v27iVY1/ZDf4meWEItEuejXX055iBw59QguvO5L3P+rR4hGm3/4cPPKbdx8xZ1EmvkcGlO6v/TA+9ZanrvjVZ69/eUG5WLRGB+8+jEfvPox0+ZOZM7VZ+D3awfYTKXwLG1Fpn8XuR44CnjOWvtiugcjIpJJYjHL/dc+0myIrvHuC0tZNr/5B/mS4bhTRzN4dOIPAm7/7HNP/WRlZx14/6V732w0RNf35iML+e+Nz3rqT1JH+ztLW5SxM9LGmCuBHwIrgPMTqWOtHROnrSXAsckbnYhI+n26aBU7N+92VWf+owsZOfWIFI3ooN3b9rJmyWeu6vj9PqJRdzudDhjRH4B9O4t45h8vJVzvtYcWMPHMcfQ7rLer/iS5NPMsbV1GBmljzHeAm4DlwInW2j3NVBER6XDeec7d7hgAn7y9kqLdxRR2K0jBiA5678UPE14jXcNtiAaYeu4EAN564p2ElpHUNv/RRXz5f85y3adXW9fuYP6jC1n6xieU7C0lO5TFgCP7M/XcCYycdiT+gL/VxpIuCs7S3mRckDbGfB/4C/AxToj29vc+EZF2bu+O/Z7q7dtZlPIgvX9Xkad6obwQ4dJwQmUHHNGPYWOHAE5wd2vJS0tbJUhHI1H+/YenWPD4ojrXy0uirHxnDSvfWUOvgd359g0X0Wtgj5SPp7UpPEt7llFrpI0xP8EJ0UuBGQrRIiLx+Tw+LOfzpf5bv9cH+U78ymRCecFmy3Xt3Zlv/vGCAw9OFnkI7qVF5VRVpnZDKGuddez1Q3R9Ozbs4i/fvJVdW9rHH2C13lk6ioyZkTbG/By4DlgCzNRyDhGRpvUc0INV7611Vcef5adrn84Nru/fVczbT7zL4ueWsHfHPnw+Hz0H9mDSmeM47tTR5OSHXPXT+9BersrXiERj/PDOy3jo+idY9+H6BveNMRw1eTjn/ewcOvcoPHA9kOV+WYQxJuXLKd5/+SPeef6DhMoW7S7hwd89xpW3XJrSMaVK7ZlnBWbpKDIiSBtjLsQJ0VFgPnBlI9szrbfW3tPKQxMRyVjHnzWu2ZnO+sacNLLBwSTzHl3II396mmik7hrjTSu28O8VW3j67y9y8e++woiJwxLv5+SRPPaXpxvsbd2cF//5Gps+3cx3b76EnZv3sPiZ99hTE+wH9GDi7LF079+1Qb2+h/Vh5btrXPXVZ3BPfL7UbgX4xn/edlV+xeI1bF+/k96DMn+Jh5ZsiGRIkAYOrX71A9+PU+ZN4J7WGIyISFsw8Mj+HHr0AD5btjHhOlO/OKnOx288/Db/+dOTTdYpKy7n1u/fw+U3XcwRE4Ym1E8oL8ikM8bx2kMLEh5bjeULV3H7jx/g8hsv5tyrZidUZ/I5410H6clnT3A9Njd2bNzF2qXrXddb9PR7nPXdU5M/oCRQeBapKyPWSFtrf2WtNc28TU/3OEVEMs1Fv/4yBV3zEyo7+7JTGHz0gAMf79y8m0dveCqhutFolNt/dB/7dya+Fnn2FbPo1rdLwuVr+3TRKha72JVk1PQj6dYn8b5yC3MY/4XRXoaWsN1bEz8mvbZMWyet9c4i8WVEkBYREW969O/GVXdeRt/D4q9JDmQHmHPVbGZdMqPO9fmPLiIWS3yLuorySn5+5u9Z+vrHCZUPhrLo3q9bwu3XN//RhQmXDWQF+OafLkjoQcVAdoBL/3A+Ofk5zZZtCbfb/2WK2sF57a49dYKzwrNIXZmytENERDzqNaA7P3vwB6x4Zw3zH1vEllXbiFRFKOyaz5iZo5h4xljyO+fVqROLWRY+vcR1X5HKCHf85AG++YfzGTV9RLPlK8orXfdRY8PyzexYv5NeCa4XPuTwvvzwrsu4+38fYuuaHY2W6d6vGxde+0WGHDPI87gS1d3jbLybmfVk0ZINEW8UpEVE2gGfz3DkhKEcmeAa5oqyMKX7Sz31ZWOWe3/5b3733DXNzgAHc7M99VFj7+f7Ew7SAP0O68M1D/2A1Us+4+0n32Hn5t1Ya+nauwsTZ4/liInDUv6AYY1eA3sweNSgRncfacqEM8amZkD1KDyLtJyCtIhIB9TSVQfh0greef59ps6Z2GS5w0Yfysp33D0EWJuXvbKNMQwbO5hhYwd77jdZps2d4CpIHz7uMPqkKNAqOIskn4K0iEg7UF5SzvuvfMyuzbsBS9c+XTn25JHkFTa+DjiUFyKvMIfSonLPfS586r1mg/Tks8fzwp2vuT6+G5xZ9p4DunsdXkYYM/MYPpr3KUteav7kxfwueXzlmnOS2r/Cs0hqKUiLiGSQ3dv2suCxxbz34lL27yrCH/DTZ0hvJp8znjEzRxEMZdUpX1ZczlO3vMDiZ99vsB75sRueZtypoznrO6eS1zm3zj2fzzDhC2N49UH329PVSGR3iU7dC5h01jjmP+Zuv2uAo6YcUefQlbbI5zNceO0XCYayePup9+KW696vG5fdeBE9+nt/OLOGwrNI61GQFhHJANZanr/rNZ67/eU6O2lEqqKs/3gj6z/eyJN/e55v/vEChowaCEDx3hJuuuz2uA/WVVZU8dYT77Dmg3V879ZvNQilk+dM5PWH33K1c4cXc6+ezZ7t+/jkrRWu6k2vt+d1WxXICvC1X8xl+pcnM+/RRSx9bRml+8vIDmYxYER/pp47gVEzRhDI8v4jWeG59awt3Xng/YpYVRpHIplAQVpEJAM8c+vLPH/Xq02WKd5Twl8vv4Mf3PYtBo7oz+0/uj9uiK5tx4Zd3HrVPXzpJ2fz1uOLWLdsI5XlleR1zuPw4w7j00WrPY050T2iA1kBvv3nC3ji5ud57aEF2ASC+ykXzWD4+MQenGwr+g/rw1d+djZf+dnZWGtp5ATfhCk4t57awbnGkF7O6ZrBFvzyI+2D/g8QEUmz9R9vajZE16iqqOLunz/EeT8929WpeRs/3cIfL/pbnWt7tu8DwPhMQuG2volnjEu4rD/g59wffIFpXzyeW668kx0bdjVaLpAd4PRvnszMC6e5Hk9b4iVEKzy3nvrhuSY4i9SnIC0ikmZvPvK2q/I7N+3m2dtfSVr/XkJ0KC/Icae6Pxmwe78u/OLRq/ls2UbmP7aIjZ9uoaoiQn6XPEafcBSTzhjXYD13jYpwFUteXMqyBSsoLy4nmJPN4FGDmHTmWAq6JHa6Y1uj8Nw6FJzFKwVpEZE0qiivZMnLH7mut2H5phSMJjHGGC689kvk5Ic81x88ciCDRw5MqLy1ltcffovnbn+FsuK6u4wsm/8pz9z2ElPOmcA53z+tReuMM4GCc+toarmGiBtt+zuOiEgbt29nEZHKiOt60apYCkYD3ft3Y++OfUSrGt+uLpiTzYXXfSmhUw2T5albXuTFe16Pez9aFeWNf7/Fri27+dafLsAf8Lfa2JJB4bl1aNZZUkFBWkSkDfL5fJ72Zm7Ors27+cFt32bth+tZ+PS77Nm2D+Mz9OjfjUlnjmPC7LFx96ZOhQ/f+KTJEF3bxwtW8NydrzL72zNTPKqWUXBuHQrO0hoUpEVE0qhz9wL8Wf64M8DxdOpZwJ5t+1IyppL9pcy6ZAazLpmRkvbdeOWBea7Kz3tkIadcNIPsevttp5vCc+ppuYakg4K0iEgaBXODjDlpJO88/4GrekOPHcLiZ5ekZExv/vttjpx0+IHDX/btLOLtJ99l04otVFVUUdA1n2NOOJqjJg/H7+EI70RtXbvD1c4kAKX7y/jg1WWMP/3Y1AzKBYXn1FJwlkygIC0ikmZTvzjJdZBe/OwSDhnej00rtiR9PKuWrOWW797FpX/4Go/f9BzvPv8BsWjdNdmLn32frr07M/fqM1K2XnrTyq2e6m1euSUtQVrBOfW0XEMyjYK0iEiaDT56AKdcNJ0X73nDVb2tq7cx6KhDWP9x8nfwWPPBZ/zmS3+heE9J3DJ7tu/j9h/dz1d/PodJZ4xN+hi8PIQJUFWZ/LXj8Sg8p5aCs2Q6BWkRkQxwxhWz2LeziMXPvp9wnWg0xqFHDWTUtBHMe3Qhe3fsr3O/U49CAtkBdm/ZE6eFpjUVomtYa3nwt48xYHg/+g/r46p9ay2ffbyJT99eSXlJmGBukKHHHsqwcYfh8xkKu3nbG7qga2r3lFZ4Th0t15C2RkFaRCQDGGOIRt1vaffO8+9z/Yv/y0nnT2PFu2vYtXk3WOf47iMmDGXn5j386ZJbKCsqb74xj2LRGK8/tIDzfzk34TofL1jB07e+1GBpyvN3Qa+B3Zl1yYkcc+LR5BbmuB77sScdnVA5GwtD5XxsZCXYMJgCTPY4yBpd5+RBBefU0qyztGUK0iIiGWLbuh2u65TuL6N4Twmde3ZixMRhDe73HtSDS/9wPn/7zl1EI6lb8vDeS0s596ovkFvQ/NZ4b/33HR783eNY2/iJijs27OLeX/6bzzftYuLssbz6r/kJj2PY2CH0GdyryTLWxrBl/4bws2DL6t4Lvwj+nqwt/zIme+SB6wrPyaPgLO2JgrSISIawHmakASKNbJ1Xur+M5+96lfdfXca+eks+UqGqIsL2zz5v9rTCVe+t48H/ix+ia3v+zlf54o/PpFvfLuzeurfZ8tmhbM75/ulNlrE2hi25ASrqHsu+dl+XWh9VMWDALZi8SyF0WrP9StMUnKU9U5AWEckQhT0K2brW3ay03++vsyY4Gonx1C0v8NqD8z0tFWmJqgQeDnzxntexseZDdI03//023/nbN/j7lf9k5+bdccuF8oJ8608XMGB4v6YbLH/0QIiuG55hwICiOh/b0jsxgUEQODLh8YrWOUvHoiAtIpIhxp1yDCsWrXZVZ+SMIwnmZAPOw4d3/+9DvP/KR6kYXrPyO+c1eX/Hxl18umiVqzZ3bNjJvh37+Mn93+XtJ95l3qOL2LXlYKDO65THpDPHMe2LE+jau0sTLYG1lazZNh/swXL1w3O9GtjyJzAFCtLN0ayzdFQK0iIiGWLMyaN4/MZnKd1f1nzhalPnTDzw/qsPzE9biO41qCd9hzS9Ntnt4So11rz/GYePO4yTzp/KCV+dwo71n1NWVE52Tja9B/UgKxj/FMPaDwraiiUMOGS7u84r34PYTvD18DT29krBWcShIC0ikiGyQ1l8+afncNf/PJBQ+QmzxzJszGAAopEorz+8IJXDa9K0ORPr7HTRmMqySk9th8sP1vP5TLMPE8bbZcOWboKw294tRNZAdscO0lquIdI4BWkRkQwy5qSjiVz7JR749aNN7rIxYfZYvnrNOQfC68cLVrB/Z1PLFBJnfIZTLj6BF//5WkIPBR4yvB8TzxrXbLmcgpCn8eTmN70TSMLb09kqT/1jvf0C0JYpOIskRkFaRCTDjD/9WIaMGsS8Rxey8On3Diz18Pl9jJoxgmlzJjF0zKF1ZoA3rfB2nHZjxs06hjMum0mP/l158DePE43GD/SHDO/H5TdeTDAUf3lFjcOPOwy/399ke40ZMfnwBtc87e3s83hQi6/AW702Rss1RNxTkBYRyUDd+3flnO+fzpnfmUXxnhKikRj5XfIOPFhYX6TK23HajTnhK1MAmDh7LIcc3o83Hl7Auy8upariYB+9BvVk2pyJTDxrXEIhGqBzj0JGzRjhah33oKMGMGB4v6QcimKyx2PLn3BZKR+yRrjuqy1QcBZpOQVpEZEM5g/46dyzU7PlknUs9pBjBtXZQq7/sD587RdzOecHX2D7+p1EKiLkd8mjz+Ceza6Jbsyp3ziBjxesoDLc/HKJSM9cjr1w8oEQ3eJDUQKHg38QRNcnXid4AhBsWb8ZQss1RJJPQVpEpB045oSj+O9NzxJzsUdzfXmdcpnzgy9grW0QknMLchh89ICWDpN+h/Xh0j+ezx0/ur9BmK7qnnvgfeM3nPaNk5h6xpgW93mQweRdhC36NZDA8hJfV0zOmUnsv/Vp1lkktRSkRUTagW59ujBi8nCWzfvUcxul+8v4/YV/Y8AR/Zg6dxLjThnV5NZyXo2YOIwf3XM5L97zBouXriEWOXhwjKmq4qjJwzn5gmkMOebQpPdN1ihM/vewJX8FmlgO4+uGKfgF+NpW8FRwFmldCtIiIu3EWd85ldVL1hEurWhROxs/3cID1z3Caw/O4/IbL6Fr787JGWC1tbv2QOcg075/CmP2TaF0x17KSsIEc4McNnoQ3fqkOPwFp2D8/bDhp6FiAXUCtekEoRMxoS+Ar+kDXjKBlmuIpJeCtIhIO9FncC++c/PX+ccP7qV0f2mTZY3PNHtU99Y1O7j5iju5+p+Xk9cpt8myTWn+QcFBntv2LDAYk/89yLsYIp+BDTu7cwSGAsmfhU8WBWeRzKIgLSLSjgweOZBrHv4+8x9dxFtPLKZod8mBe/4sP70G9iArGGDDJ5sTam/Hhp28ePfrnPP90xMeQ/3gDEl4UDBVTCFkjUr3KJqk5RoimUtBWkQkBay1VJRVUlVZRU5+iEBW63277dyjkNmXzeTUb5zAjg07CZdWkpMfotegHhTtKubnZ1zvqr2FT7/HF749k+wmtrlLxvZ04lBwbhvCkdXEbMuWUUnbpyAtIpJEZcXlLHp6CfMfW8SODU4g8vl9HD31SKbNmcDhxx3mads4LwJZAfod1qfOtfdf/ohYNBanRuNK95fx6aLVjJp+5IFrbWrWOcNpuUbmC0dWN7g2uLAHQb9iVEen/wNERJJk7YcbuO2H91Kyr+765Fg0xoevf8yHr3/MqOkjuOg35yV8iIlb1lpWvruWRc+8x55t+8BAj37dmHTmOAaPGsj+Xd6OEd+3c79mnZNIs86ZLV5wFqlPQVpEJAk2rdjK375zJxXlTR808uEbn3DnTx7g23++EH/Al9QxbPhkE/f+6j9s/+zzOtfXvP8ZC59+jwHD+3HI8L4Jt1d7X+fdJkp/FJ69UnDOXArN0hIK0iIiLWSt5cHfPdZsiK7xyVsreOf595k4e2zSxrB26Xpu/s5dTZ4YuHHFFrav/zzufagbngGodNo7csyhCtEuaLlG5lJwlmRSkBYRaaENn2xmw/LEdsGoMe/RhUkL0uHSCm67+r6Ejt2uDFfV2fouXnCurc/gXgwe2fJTDdszBefM1FhoBgVnSR4FaRGRFlr83Puu62z4ZDPb1++k96CW/0B/5/n3G6zLbkpl15x6F5oO4DPOmwy0zgOSbYmWa2QezTZLa1OQFhFpoX2f7/dWb8e+pATp+Y8vbvJ+Y7POOQU5lBeXN9v2uNNGc/xZ41oyvHZDwTnzKDhLuilIi4i0kM/vbbbW+Fv+sGEsZtm6enudaw2CMzSYdfb5DONOG817zy/F2oYnHPoDPqZ/aTJnXXkqHXU2Wss1MotCs2QiBWkRkRbqOcD9D3NjDD36d2tx3zYWw1qb0Frn2qJVUS669st84ZszWfDYIla/v46K8gpC+TkcNWk4k84aS2G3whaPr63RrHPmUHCWtkBBWkSkhSadOY4X737dVZ0jjz+crr07e+6z9p7O/oGdqSqtbDY811bQLR+A7v26ctaVp3keR1un4Jw5FJylLVKQFhFpoR79u3H0lCNYNv/ThOtM/+Ik1/3EOxClS5dctu0tcdXW2JnHuO6/PVBwzgwKzdJeKEiLiCTBV645lz9dfAu7t+1ttuyJX53CiEmHN1sukZMES/eXsXPz7sQHWu34s49zXact0jrnzKDgLO2VgrSISBJ06l7AVXdexh0/uZ/1H29qtIw/4GfW10/gtG+c2Oj9+sEZmj9JcNEz7xGpjLoaq/GZpJ+qmEk065x+Cs7SUShIi4gkSZdenfjR3Vewdul65j22iI3LN1NVUUV+l3yOmXEUk84cR6fuBXXqJDLr3JRNK7e6HqeNWbau3dFuHiZ0G5wtFRB+C1vxCsS2gY2BrwcmNB2CMzAmL4WjbX8UmqUjU5AWEUkiYwyHjT6Uw0Yf2uj9lgbn+iIVVd7qVUZa1G86tWS5hq1ahi3+E9jiujeixdjSdVD2L8i7DBOcmoyhtksKziIHKUiLiCTJhuWbWb5wFeGSMNm52Rw+dgj074Sptw1zS8Nzbfld8r3V69x2Zl2Ttc7ZVi3DFl0HNLEUxlZgS24EopjgDNd9tEcKziLxKUiLiLTQJ2+v5JnbXmLDJ5uBWgeiPPYWPfp35YxLT+TYk0ampO9jTxrJ/McWuarTrW8XBhzZPyXjSZZkr3O2VGKL/0yTIbp2+ZJ/QNZIjK/le323JQrNIu4oSIuItMBbT7zLvbc9h7VATYCutZ/zznXbueun/2LX5t3MvCj5M5zDxg6m96E92f7Z5wnXmXz2eHy+zHrYMOUPCFa8BbbIRYUINvwyJvfLCZW2sT1QuRAb248xAfAPhOwxmAz/MavgLNIymf0vXEQkQ63dtYcNyzfz8O3VIbqZw1CevOUFehzSjdEnJntm2jDnqtnc8r27sbFYs6X7DO7F1LkTkzwG91p7WzobfsV9pYpXoJkgbaPbsGUPQOViwPnvf+DAdV8XCJ0OOWdhyIxfXBScRZJLQVpEJAGNPST4xJ+exIYTP03wuTtfZfSJRwOm2bJuHDFhGJf89jzu+cXDRKviL13oM6QX3/nr1wnlhZLaf8m+Uj584xP27yrC5/fRd3BvRhx/OP6Av065tG5LF9vmoc4eLFUYshq9bSPrsEW/AhvnMJzYXidkR1ZBwdVpmZ2uH5wVmkWSS0FaRKQRze2u8fnGnax4Z42rNreu2c7q9z9j6LGDWzy++o49aSR9D+vNGw8tYPHzH1BZfjDg9xzQnalzJzLpzHEEc4It6KUSKhZhoxvBRigvC/HcveXM/++aBruAdOpRyJEXHMuE04/FVC8jaZv7OTc+y29tEbb4N/FDdG2V72BL78PkXZLksdWl2WaR1qcgLSJC/MNQtq7ZxpKXP2Le7hL8WX76D+3D2FNGsfr9zzz188bDb6UkSAP0HtSTL//0HM763unsWP85VRVV5HXKo8/gnrRsFrwKW/YohJ+vs21cjg/OuhCGDs/nv3d2Z6v/4A4iuwgz75G3KfpkC9/84/kEAmn+cePrDrF97uqYfCC78Xvhl9y1F34em3MuxtfJ3RiaalLBWSTtFKRFpMNqatZ504ot/OWbt7Lmg4aB+fGbnuGQw/t56nPdRxs81XMjlBtk4JGHJKm1KmzR/0HVBw3urK0oBAt5x8KcP+3j3zdns/ujuktLPl6wgv/84Sm+8rNzkjQeb0xwBjbi7i8IBE/ANPILiCWGDb/kcgRRZ811zrku6x2k4CySeRSkRaTDSPQwlNVL1nHL9++mKs7654qyykYDdiKKdhezde12+g7p7al+a7Mld9QJ0Wsr6p6GOLj7PuedbvDDn+7nt98aSGlR3bXRbz/5DrO+fgJde3VO8WibEJwOZfeDDSdcxYROafxGdAfEdrkegq36GOMiSGt9s0jmU5AWkXbLyymC+3bu57ar740bopNhz7a9bSNIx3aztuhd4GB4HtxtX9zihV2iTJq1n5f/U3ctdCxmWfD4Ys64LE4wbQXG5EDeFdiSPydWPvd8jL9P4zdtubdBNFFPs80ibZOCtIi0G/HWObsx/9FFlJckPmvZ3tTeWcOGXwRiTYbn+iafvp9XH+1CLFZ3ScSq99YmaYTemeDxQAxbcjMQ74h0g8n9GuSc1URDuR4HcLCegrNI+6AgLSJtVjKCc23RSJS3nninJUNKSPd+mbV7Rbxt6WL7l0Nkn6u2uvWK0LlHhD076m4ZF86QX05McApkHQUVr2DDLx9couErdNZEB2di/M38tcDfC/y9Ibo94X7DxDCBfphaAVrBWaTtU5AWkTbFy3KNRO3cvJviPQlsZ9YCg44aQO9De6Wodcu6jzayde12opEonboXcuTEYWSH6u48kfB+zi7WE9cWymm4ZVwoP7l7V7eE8XWBnLmYnLlYqpxrcfaKbrQ+BkKzsKX3xC0TbrBtXhaDu56C8eU3Wl5E2iYFaRHJaKkMzvVVhatS1naN1JwqaHn7yXd57aEFbFu7o86dnIIcDj/vaCbOHkdOQQ7gYj9nXw7EP98lrvLShqf4DT9uqPuGWoGbAF1H8CQIPwdR52j2+sF5SE6948hz5ihEi7RDCtIiklFaMzgDxGIxVr27hs837aZ4r7fZ6EC2n0hl84nz2JNHctypx3jqIx5rYzzw60dZ9PSSA9eqBhycga4iyrsvLGXz/FVc+fdL6da7S8Jtm+wx2KqPXY1n6/ps9u6s+6PF5/Mx+ZzjXLWT6SqiW7C552NLbge7v2Fwri00A3LPa73BiUirUZAWkbSqCc7WQqQyQiA7wIDBbsKzpaqiiqxgFm4OHYlGorz+0ALefGQhe7btdTfoek695ETefXEp2z/7PG6ZiWeM47yfno0xDWdrW+KpW15k0dNL6oRngMCeujtE7NxTzi1X/pOf3HclwVCCs7DBE6D0QSDxmfr5z3Si/tdhypwJdO6RvINIWlv8BwN7YAt+CeX/hop5YCvqFvL3h5zZEDwJY5J7LLyIZAYFaRFpVbVnnKNRy7oPN/DpvGWsWLyGWDSGz+/j8OMOY+qciRw1eTg+X8PgGYvF+HjBCuY9upCV7yRer0aksopbr76PTxeuavHnE8oNMuMrk5l50YwDY1r/8UYqw5Xkdc7nmBkjmHLuhKRvd7e2dCdlxWU8P38RsQHZDYJzY7Z/9jnvPv8+k88en1AfxhRgc86C8kcSKr9jcxaLX6m7z/QxJxzFuT/4QkL1M4WbHTWMvyvkX4bNvRAql4DdC2RBYCAEjlCAFmnnFKRFJOUaW65RvKeYW6+6l/WfbKpzLxaN8enCVXy6cBUDj+zPt2+4kMJuB8NZ0e4ibr3qXjYs3xy33qARh/DtGy6koGtBo+N54NePJiVEA5x66UkEc4IAjJx2JCOnHZmUduur/4AgwNYFq/F9XoqbOe43H1nI8Wcf1+iJfY0xuV/GxvY6p/I1Yee2ALdc04/KsDOabn27MP1LxzP9y8fjb+KXmkyQjK3ojC8XQlOSNSQRaSMUpEUk6Zpb51xeUs5Nl93OtnXxl0IAbFi+mZsuu4Mf3nUZuQW5lBWX8dfL72i23vpPNnHTZbfzw7suJyc/p869bet28O4LSxP/ZJpw8oXTOOlrqQlPjQXn+g8JPrlwpet2t6zexv5dJXTu3vgvGfUZDORfBoEjsOGnIFrviHOTR9Q3lU1bhzNlbpRAlp/eh/Zk+PihGRugtYeziCSLgrSItJjbBwSfvf2VZsNwje2ffc6zt73C3KvP4NnbEq+3bd3nPHv7K8y5anad6/MeXZhQ/aYMHTOYE74yhZFTE599Lt1fxuJnl7B1zXYikSiFXQsYc8ooBh7R/0CZhLelq+b14JjykvKEgzTUbPc2A0LTIbIaIhuACPg6Q/axZBFk7ExPQ2kVCs4ikioK0iLiWkt21qgIV7Lo6fdc9bfomfc45ZIZLHrGZb2n32P25acQrLWP8qceZnGNz3D+L79IdjBA38N602ugu8/38RueYdGzS4hU1j1N74X5i+g7uBcnXTCNPoN7J74tXbVgTnbzhZJYz2AgMMx5y2AKziLSWhSkRaRZyTxBcNmby13PpIZLK3ju9lcIl1Y0X7iW8pIwy974hLGzRte55paNWUZNO5JQnrtDRcJlFdx8+R0H1oHX31kD4PP31vPIsi1c9peLwGWQHnrsYNZ9uKH5grX06N+Nzj3b7g4ajVFwFpF0yZggbYzpD1wHzAK6AduAJ4BrrbUt25tKRFxJ9tHbtXndam7npt2e6u3evq/Ox8HcICX7yly1YYxpcDpgIh787WOsLt4BtQJ0Y7trVFVUcfuP7uMXj/zQ1TZxk88Zz8v3vkEsZhOuM+XcifjawE4SNrIJIh+BLQeTB1mjMP6+QMPgrNAskrmSke+MMW8A05ookmNtw6NYjTFHAr8CpgOFwAbgYeB6a23zWx0lICOCtDFmCPA20BN4ElgBHAd8D5hljDneWuvtp6iINCuVwbkBjyHO+DzWq9ff0DGD2b11SZzSjesxoDvvv/wh3Q/pxqARh9DUftU165z3fb6fxStWJLQtHTiz7vMfXczsyxJfbNytdxfGnz6GhQkulSnsXsjEM8cm3H462KoPsWWPQGT5gWsHTg0MDMWETsb4D1V4FmkDUpDvro1zPVL/gjFmPPAakAU8CmwCTgB+AZxojDnR2vqbv7uXEUEa+DvOf+QrrbU311w0xtwA/AD4LfDtNI1NpN1p1eBcT88B3T3V6zOkF58ucr9lXc9DutX5eOqciXVOAUzE5xt2cvfPHz4wjulfPJ5JZ43D5/PF3V3jv/9ZjH+Pu5nvt55YzKmXnkgg4E+4zpf/5yz27tjHinfWNFkur1MeV9x0MXkFOU2WSycbfhlb+o8Gx21DzZHbSyD6AeR8D1CQFmkDkprvrLW/SqScMcYP3A3kAmdaa5+qvu4D/gOcW93/9Yn2HU/a9yaq/m1lJrAeuKXe7V8CpcD5xpi8Vh6aSLuxdteeOm/gBOfab63lqMnDKeia76pOfpc8Tr/0JPI757qqV9A1n6OmHFHn2sAjD+HISd4flttYtZf7/vUMN/z+PlYVbQec4Fz7DeCzj92tXQYo2lPCbpdLX7Kys7j8pouZdckJ5HVq+G3S5zOMmnEUP7rncg4Z1tf1mFpDOLKa8vAzlJfeQpgYQ3KKGrwdFIOSm7BVn6ZtvCLSvDTnu2nAEcC8mhANYK2NAT+u/vDbJgknJmXCjPSM6teXqj/BA6y1xcaYt3C+EBOAV1t7cCJtUTpnnJsTyAow+ezxPH9X4v+cJ589nlBeiMnnTOCFf77mql4gq+G3uUt++xX+esWdbKx3qEs8jR2/ve6lj1kcDHHyhdN55M9Ps/Kd1ZSXhgnlhTh83GGUFXlbflcVTvw47gPjCQQ447JTOPXrJ7D0tY/ZsnYHsUiUwu6FjDl5JF0y7OHCxtY4231/hjqBuSkxKHsUOv08+YMTkWRJer4zxnwJOBSoBD4FXouzPOOE6tcX6t+w1q4zxqwChgGDgbWJ9B1PJgTpw6tf4/3NdjXOf+hhNPMf2hgT7++1w70NTaRtyOTg3JhTLp7OyvfWJLTjxKEjBzDrEuf78axLZrDyvbV89lHz9QaPGsgpF09v9F5Ofg7fv/WbPP2Pl1j41LsNdgNpLDg3ZuHT7zWyPnk/29btaHZ88bidda8tKzuLcbNGM85zC6nR3MOBNrIOIi6X7VR9gI1swwT6tHR4IhLf8HjZylo7ppm6Sct3tTxc7+PPjTFXWGsf9dD3sOq3Nh+ka6ZK9se5X3O9c+qHItI2tLXgXF9WMJsr/vp17vn5QyybF/9P9EdPOYKLfnMeWcHsA/W+c3MC9aYewUW/PlivMcGcIHOums3sy2by/JuL2Ve9znjPdmdpRaIPCSbTgCP7u9q1I1O53o6u8kNvHUWWgYK0CEQNlCT+bEXCbbZMMvPdk8CfgA+A3cBA4ELgh8C/jTGnW2trzz63WrbMhCCdNPF+O6r+berYVh6OSNK09eDcmFBukG//+SI2rtjMvEcWsuKdNYRLKwjlBRk+7jCmzJ1Y59S/+vU2fLqZ+Y8sZMW7teoddxhT5jRer77aDwkePeUIBvfqwg8e+jmBCvdLK5Jl6pyJaeu7JVq8HZ3XXaisu4c5RcS1FQnMPKectfYv9S6tBH5mjNkK3Az8H40s42gNmRCka34riDcNU3N9X+qHIpIZ2mNwjmfA8P587edzXdcbeER/Bv4i8XrNHb9dVVlFZRpD9IAj+jHulFGt2qfFQnQn2GIw2eDvjSGr2XpJ38fZeNxJxHhfBiMiKdca+e5O4C/AMcaYAmttcSv2DWRGkK45rzfeY/RDq1/d73sl0kZ0pODcWpoLzvUFsgP4fD5isYZbr6Va/2F9ufzGi8nKbj7EJoOlCsJvYMPPQ3T9wRsmHxs8ERM6FeM/+P9fyg9AyT4avEwuB45K7jhEJJlSnu+stWFjTDHQBcgDaoJ0q2XLTAjSr1e/zjTG+Go/2WmMKQCOx/kWuygdgxNJBQXn5Iu3n3OiDIbBoway5oPPkjmsA3oO6M7nG3fVuda1TxemnDuBaV+cSCgn2GT9kv1lLHrqPZYt+JSy4nKCOdkMOeZQppwznu79Ev88bWwftug3EF3XyM0SCD9JefgZTN4FmMDB57RTeQCKCRyGDRwGkab3wq4jayQmkJnb+YkI0Ar5zhhzOE6ILgZqf4N9DbgG5zTF/6tXZzBOwN4ANPKN0J20B2lr7VpjzEs4T25egbPWpca1OL9h3GatLU3H+ESSQcE5uSJVET7fsJO1ZbsI5WbTpXdnjPG5Cs6NmXLuhJQF6fGnj2HcrGPYtm4HkcoIBd0KOPToAfh9TW/nH7OW5+54hZfufYNIZd3Du9Z9tIFX7n+TsaeM4rxrziXUzDHm1oaxRdfVnYWGRg5AiTE4djPk/AqTdWSin2LL5HwRin+XYGEf5LpfDiQircdLvjPGDK+uu6LWtUOB/dbaOj9IjTE9cA5dAXjYWlv7G+SbONvjTTXGnFHvQJbfV5e51VprW/p5pj1IV7sc5wjJvxpjTsT55Mfj7EG4Cue3CpE2Q8E5NZZu/oz3X/6Qj974hLKS8IGdNXoc0o0p506k71njyMkLeW5/9IlH8eztDWeOk6FLz05079uV7n1dzB5j+ff1TzD/8fgTNtZa3n1hKXu27+O7f/sG2cGs6utFULEIG9uDMX7wD8BGt0B0fRMnB9ZTege20w0NjllPBRMci41dCqV3NFPSB/lXYLJGpHxMItJibvNdzXZMtb/pTANuNcYswJlB3gMMAE7DWev8HgcPWQHAWhs1xlyMMzP9qDHmUWAjcCIwFngLZ211i2VEkK7+rWUscB3ONPxpwDbgJuBaa627o75EWpmCc2rUXq6x8dPNPPaXZ4htdZ4hqf3Na+em3Tx+4zMseHwR3/nr110tdagtEAhw+U0X85dv3sb+nYkeDtK8YG6QUTPcB7/3XvywyRBd29ql63nq7y9w7vcmYssegIq3AWeCpvxAcDaAMwHTaHCuL7IBIishq3W24jc5p2L9vaDsP43vKx0YAblfxGQf3SrjEZGWSVK+W4Kzf/QYYDRQiLOUYxnOcd+3WWsrG+l7sTFmHM7s90ygAGc5x3XA9XEOcnEtI4I0gLV2E3BxuschkggF59Rp7CHBTSu38sT//odYM7tqfL5xF3+94k5+fM8V5Hf2dupsz/7d+dHdV/DoDU/z0RufEIvV/cufP8tPtz5dXM1ajz91tKeZ8tcfWuCq/FtPvMPpX3oCG9zd4F5CwbkxFW+1WpAGMNnHQvaxziEtVcsgVg6+PMgahQkMaLVxiEhyuMl31toGf/6y1i4DLvLY93IgpevAMiZIi2QyBefUSWR3jfuve4SqBLem27VlNy/d+wbnfO90z2Pq2qsz3/z9+ez9fD/vPPc+e7btw/gM3ft347jTRuMzhj9ecgs7NzUMrPX1OKQbp3/7ZNdj2LRqK+s/2ZRw+Z6HlQPlLH0vzKjjWxCc60vTHwRNYDAEBqelbxGRRClIizRCwTl13G5L9/bT77J51VZXfSx8egmzL5vZ4u3kuvTsxCkXzWj03vf+8U3+/r1/snVt/OPA+w7uxeU3XUxB53zXfTfVLtQE54MCW5y/UkbXRBhyUvKWpZDAvtIiIh2VgrQICs6p1JJt6UqLy/n39U+47rN0fykr313LiOMPJxqJEQgk+ehcnFnrn9x/JR+8sox5jy5k3UcbDtwbPHIgU+dMZPRJR5OV5e3bbDQSrfNxvOBcXyzS6GXvAoOS3KCISPuhIC0dUv3grNCcXG5nneNZ/MwSqiq9JcMn/vY8d/z4fqoqI2QHsxg+YRhT50xk+PjD8CVpF4qsrADHnTqa404dTUW4ioqyMMHcEMFQy2dxO/XbVyc8xwvO9RV2S2aSDkCw8Rl5ERFRkJYOQLPNqZes4Fzf/McXe667dc32A+9XVlTx0Zuf8NGbn3DY6EP55h8vIL9Tco+XDoayWhSg658eOGhEf7qGsyjaXeKqnTHTipsvlKjAcCi5GRvbBfjA3w+CJ0PWUa2yJZ6ISKZTkJZ2R8E59Vp6imAiIpEoO9Z/ntQ2AdZ88Bk3X3EnP7j9W4Rymz5NMJVqB+fivSV8+MZy9r2zjcpwFbkFIY6efATjTx/Dy/e9mXCbR4wppWffZM1I+yHycd1Lkc+gYgEEBmDzfwi+blD5DsT2QvVe1WSNxDnzQESk/VOQljZPwTn1WiM41xept0Y4mTat3MILd73GWd89NWV91Fd/xhngkGBn/v2HJ1n0zBJi0bqHpHy8YAWFXQP0HhBh+8bmv1Xn5MU491sNv07eNfHfP7IR9v0QZ1/qerup+HtiQ6dD6HQFahFp9xSkpc1RcG4dqVqukahgKItgbpCKsqTsmd/AW0++y+nfOqnFO3s0pX54HlzY48D7VZUR/v69u1n57pq49UdN2sWsL+/hH7/ox+Z18WfP8ztFuOy6rfQZkNgWgQ4f5F7ozDrHisFkgb8/hF+hQThuVJyZ7+jnUHo3VH2KLbgKY/RjRkTaL32Hk4yn4Nw60h2c6zMYxpw8ireffCcl7ZfuL2XZ/BUce2LyTslrKjjX98w/XmoyRANMOX0/nbtHufrGjbz3RgHznu7MxtUHD3bp1quKyafvZ9Ip+8nv1PDY7yaFTsXkzgZmH7hkyx4hsRCdgMpFUHoP5H8jOe2JiGQgBWnJONpRo3WkY7mGW9PmTkxZkAbYs21fi+o3tlyjqfBco6KsotkHKbOCln6HOqfeZmXDxJnFTJxZTNFeP2UlPrJDls7dI/gaPPPnA5oJ1dkTIe+iOpestVD+XLNjdyX8IjbnHIw/s/6/EhFJFgVpSSvNNreuTJt1bs4hh/dl6tyJzHtkYWo6cLnxhNfgXN97L75BuDTcZJns7MbDcGGXKIVdmli/bAogOAEq3gBbb1mMvxeETofQaQ3XL0d3gt2fwOjdiELFy5D7pSS3KyKSGRSkpVUpOLeuthacGzP36jOIRWIs+K/3rfDi6d6v+f8ebpZrJMJGPmPLx08BTZ92WF7qJxKBgNvv0v5OmPxvYXMvcHbUsHuB2jtqxPntoeJVlx0lqPJDBWkRabcUpCWlFJxbV1tYruGW3+fjvJ+dzbEnHc2bjyxk2bzlxGLWuZflZ8zJozj+rHHc9sP7KCsub6a1gwq75nPU5MMbXE92cK7N2koo+h2RSPO7WcRisGxhPqOnuNtHmqzxABhfDoSmJTiumDODnRKJf01ERNoaBWlJKq1vbl3tMTg3xmAYftxQhh83lJKiMvZ/vh/j89GlVydy8pyH7yaeMY5X/zUv4TYnnzOBQCCQtOUaCal4C2K7Keic2Ndo3jOdGD2lBEuiq1B8EJrpflzRbRBL5tZ5teWkqF0RkfRTkBbPNNucHu1huUZL5Bfmkl/Y8FTC0791EqvfX8vGT7c0Wb/nYeX0G9aH6Rf0PxCiUxac6wu/CMCxU4t5/l/dmi2+6sNcPlyYx6iJpYmF6ZyzMP7m223Alrmvk6is5O2KIiKSaRSkJWEKzunR0YNzokI5Qb57y6Xc9T8PsOKdutvK9Tzs4PKCIccM4ns//iqhvNY91dBaC5F1APQdWMXQkeWs/qj52dp7ru/NN/53GyPGNRN2Q7Mg96veBmdSNWvscYZcRKSNUJCWuBSc06OjLNdoTFVlFUteWcb6jzZQUVFFXmEOI6eNYOixh2ISWNyQV5DDd2/5BmuWz+f9Vz5i4/JNVIQjBHNyGT1oMFPnTmTgiP7xH7hLKUvtQ0zO/eZObvjhIVRWND2Wygofj981ksMmHEXQvOoc011b1tHOThzZ47x/Xv4+znHfsd3e6scTOsnbDLmISBuhIC2AQnO6dfRZ55i1vHDXa7z20ALKiurOvL724AL6DO7F2d89laMmHxG3jdprnQ8Z1odpY0embLyJsrYKKhZBxSsQ3Vzn3iGHVXD5b7Zw26/6UF7qj9tG7wFRvnPzpYS6dMHaUyG6CWK7AB+YPIjuALsPKhZgs4Zj/O6XqRjjx4ZmQtlDruvGlT0W8r6evPZERDKQgnQHpeCcXh09ONcWjcW45+f/ZslLS+OW2bZuB/+46l6+9vM5TJw9Fkjt7hrJYKtWQfEfINbw31qNoUeX87+3bWD+c515+/lCivYe/Jbce0AlU2fvY/wXppDTowuAM+McGICNGCh/DCrepu5R3QabPRZyzsVkDXM34NApEH4eYvsSK+/v4+w9Xf+ocF9XCJ0GOWdiTPxfEERE2gMF6Q5CwTm9FJzje/GfrzcZomv0GFLGSw/fT69hYfoO6ZVxwbk2W7Ua9v8CqGy2bOfuUWZfsJtTv7KbXduyqAj7yM2P0r1PxFnM0vnUum2H50HJ32gQYJ27UPkuVC7B5n8Xk+D2dwDGV4gtvAb2Xwe2uPkK0e0QnAyB4WCLgICzV3X2sWkL0DZW6mzjV7UUYmVgQpA9EoInYHwFaRmTiLRvCtLtlIJzenXkdc5uVFZU8dpDC+Ler/2QIIB/U5iV//mQyf/n8aG6Wrat3cGG5ZupqoyQ3yWPI8YPTcoDiNZGofhPJBKiawsEoPchVXUvhmZjAn2cdiPboeQfEFmWQGsxKLkZ6+uKyU581wwTGILtdD2U/6t6trspFirmOzPYhf+LMVkJ95Ns1loo+zeUPwnUO82x6gMo/Rc2dDrkfU2z5CKSVArS7YBCc2bQrLN777/8UZ010fWDc2BLRf0qLH3tE4p2FVPY3dsM40dvLueV+99kzdL1da6H8kKMP200p1w8g849O3lqG3BmhJOxJ3PoZMi7EAAbWQ/7fgkkMFN8QAzKHoTs/3PVrQn0wWYfn0CQrla1DEofhPwLXfWTLNZaKP0HhF9polQEwk+C3YnNv6rh8egiIh4pSLdBCs6ZQcG55bZvez+h8FxbNBplw/LNHD01/oOH8Txz68s8d2fjgStcGubNRxay9PVPuPKWb9BnSC/X7QMtP2o7azSEToXsMRhjnOUK+3+NuxBdLbISG/kMEzjUXb3yp92Vr3gJm/sljC+UcBUbC0PlfKhYCHY/kAWBwRA6BRMY6KLvV5oJ0bXLvg2BoZBzZuLti4g0QUG6DVBwzgxarpEctR8SrKqsajY4N6Yy7G7ZBMD8RxfFDdG17d9VxM1X/pOfPvBdCrrku+6H6Db3dQAKfgqBQzH+7nWvV7wGdq+3NgEql4CLIG0jmyCywl0fthwqF0DopMSKh1+G0vvAlta9EVkF4RewWaMg//sYf9N/GbDWug/95c9iQ1/QEg8RSQoF6Qyj0Jw5FJyTo6ndNfqaAlZ6aDO3kZMNm1JVGeHp215OuPy+HfuY/8giTvtmYsGwLuuhDhA4DOPvUrcla6H8GW/t1YiVuCsfWe+tn8jGhIrZ8qeg9J6mC1V9CEXXYDv9DuMrbKLPTxtsK9is2C6ofB+C49zVExFphIJ0mik4ZxYt10iORLemGzntCF5/OP7Dho3J65TLYccMclVn6avLKNnrLlAu+O9iTrlkBv6Ay5lLX3cPs9JBaGxXidj+lq+3Nokvt3A0thtIIpr/K4GtWt18iK4R3Qolt0DhT+OXqX84TaKi6wEFaRFpOQXpVqTQnHkUnJPD657Ow8YOofegnmxf/3nCfU2cPZaskLsdIj552/28976dRWxetY2BR/Z3VzE43XkAz43QVIyp++3YWuvMzLZU1pHuyvs6e+vH16X5MmGXs+uV72Ij2zGB3nEKeAz9tqr5MiIiCVCQTiEF58yj5RrJUT84g7cDUYwxnH3ladz6w3ud4NiMTt0LOeGrU1z3U1ZU3nyhZNULHu/MuiayF3ON0Kw6H9rKD6D0LmdWtiX8fZ0jxN3IOgpMYfXe0C5kH9/kbRsrTnwnkNoqXobA+Y3fMx53V/G1YFcWEZFaFKSTSME5M2nWOTlSdZLg0VOP4KvXnMuD//c4sWgsbrlO3Qv5zs2X0LlHE2tm4wjmZnsaW8hDPWOysfnfgeLrSWi9dM45dXbVsOH5UHITEP+/RcJyznVOQ3TBmCxs6CQofzzxSllHYwLNzNxHtwFRV2Nx6m2Kfy97LJCNuz27fZA90f04REQaoSDtkUJz5lJwTo7WPIJ70lnj6DOkF6888CYfvrG8TqDOLcxh4uyxnPi1qZ5CNMCQYw5lycsfuaoTygvRd2gfT/2Z4DgsV0PxTTQZ8nLmQO55Bz60kY1Q8leSE6LnYEIzPNY9EyoXJTYjbkKQd1ECjXpdhhG/nvHlY0NTIOxiy8Hs8Ri/vieISHIoSCdIwTlzablG8rRmeK7v0KMHcOnvz2ffziI2Lt9MZbiKvMJcDhs9yPWa6PrGnz6aJ//2PBXlic9cTvjCGII53mayAUxwIjZwRPU+xy8ffGjQ5EJwGoRmYQKH1K0UfhpPs7b1hU7G5H3Fc3XjK8AW/hKKfwORJmaETR4U/jSxfapNAmuoG9Pc2uucLzu7cMQS2CLQ5EPu17yNQ0SkEQrScdQPzgrNmUPBOXnSGZzj6dyjkM7TXD4g14yc/Bymf+l4Xrzn9YTKh3KDzDiv6TW/iTD+zpA7B3LnYG2VM7tqQo0ut7CxMgjPb3Gf+A+BvG+0uBnj74Et/D1UvgHh5+sGal8XCJ7k/DLgTywgm0AfbGAIRNa6G0iw6TXxxt8NW/grKPq1s7VdPL5OUHjNgSPXRUSSQUEazTa3BVqukRzJekiwLZp92Ux2bdndYImHMXD4sWUcMqSCQFaM8pIgx8z6Ij36d0tq/8ZkgWliZj26AXdrfRvh7wWF/+v0lQTGF4LQLGzwFIjuBEqBIPh7NthlJCGhU6Hkb4mX9/eBrFHNjzNwCLbzn50TDitehGitXWB8XSE0E4KnNHvAi4iIWx0ySCs4Zz4F5+TJxFnndPD5fVz8m/PoP6wvrz+8gKLdJUydvY8Tzt5Lj7711+Fejy0eDzlfwQT6ts4AbQtCtAk6y0Vyv9L0ASZemzcGAkn4HhmcChVvJrg9oA/yvpXww5LGVwC5Z2NzznQebLRlzvptf1+dYigiKdNhgnRFJHIgQCs0Zx4t10guhefG+fw+Trl4Bid+dTJ7P/s/undrOEPviDpbtVV+iC38BSZraCsMzmMADgx3ZqF97k57TAdjAtiC/4Hi30NVUw9/ZkPBVZjskR768EGgn/dBioi40GGCdHZ2lgJ0htGsc/IoOLvjr3qM7t2WNl/QlkLRb7Cdb0x4LbD3QQ0Cf8+6yxISkXNWmwjRNYwvB1v4C6hcDOEX6s5OmwII1ay91v/DIpL5OkyQlvRTcE6ejrzWuaVsrBzCT7moUOwEvrzzmi/bAsYYbGgWlN6XeCVfd8gek7pBeWRj5VC5EKJbAAu+bpA9+cAaZWN8EJwIwYnYWJFzFDrZ4O/mbe21iEia6DuWpIyCc3Jp1jlJKt8AG3ZXp+JlbO6cpD3EF1fwFGdP5OiWxMrnXphR639tLAxlD0LFq2DrnQpZeg82eDzkXlBnH2fjK/S+rEVEJM0UpCVptM45+RSeU6AykQfd6ontg+hmSGS/5BY4sOyh6NpmDkMxkH8pJtTyLfqSxcbKoOiXTWxvF4WKeVC1HFt4HSbQu1XHJyKSCgrS0iKadU4uBedWUH+mNNX1XDL+HthOf4DwcxB+qd7eyH4IjofQGZisYa0ynoSV3JDYHtGxXVD8G2znv6R+hl9EJMUUpMUVBefkU3huZcbjg3kmJ7njAGxkHURWO1vfmQLIPhbjK3QeHsydg8052wmnsf1gssE/0DnkJcPYyFrndMFERbc6u6KEpqVuUCIirUBBWpqk5RrJp+CcZtkjnQfh3PB1cU4MTBJbsRDK/wuRNfXuBJx1xDlfxAT6OOufq2eebXQ3hJ/HVi6oPg47AP4BEDoFghPSO7sbfsFDnecVpEWkzVOQljoUnFND4TmDZE8Fc5+7pRrBk5K2m4QtfQjKH4lzN+IcWFL53oH9q621UP4YlD0MxOoVXw4ly6GsG7bwfzCBIUkZo2tVy93XiazC2iot7xCRNk1BWrRcIwUUnDOX8eVgc86CsocSq+Dr7BxtnQQ2/FITIbp2wZr9q/8M4ZebrxPbDft/ju30W0yKH4hslNtdUGrXU5AWkTZMQboDUnBODYXnNiRnjvPQW/jlpsuZAii8Jinrkq2tgrJ/u6hQDGX3Q8X8BMuHoeRGbKcb4x6rbSPbILbd+cDXAxPon/h4mmJygL0e64mItF0K0h2AlmukhoJz22WMweZ9GwKHQflTjezbHIDgJMj5coNt2qyNQGSdE3RNCPyHJnayYMU71WubXahwuZY7sgmqPobso2uN1zoP9oWfg8indYrbwDAInQbBKXHDd0ICw5rZrq+xOoN1+IqItHn6LtZOadY5NRSe2w9jDIROxgZPctYaR9Y5u2f4OkH2cc5BIbXYWBGUPwcVL9cLxNnY0BRnS7pAEw8kRpZ6GGXEfZWKVw4EaWujUPI3Z911o82vgpJVULkYW/B9T+uVbWQbVL7rfpyRjdjIRkxggPu6IiIZQkG6nVBwTh2F5/bNGANZI5y3OGxkMxT9GmIN/7oDlc5phOE3sQU/wAQnNt5IrCw5A25OdPvB90vvih+ia6tcCCUhKPiu+/5KbnbWdLsWgfL/QMHVHuqKiGQGBek2Sss1UkfBWWqz0X1QdF29g1EaE4HiP2PNrzDZRzW8bUKpGF5cNrLZ3bZ0Fa9jc07HBAa76GMdRFZ4GF1Nn4uxuXvqHBkuItKWKEi3EQrOqaXwLHGFn0ogRNeIQdk92Kw/NlxznHUUVLye9OE14K/+fzf8kvu64Rcg/3IX5V9130cdUahaCv4TWtiOiEh6KEhnMC3XSB0FZ0mEtZXuw2JknXPQStbQuteDx0Pp3WBLEm/L37vuUo1EBE90XisXuasHULHIXZCObnPfR322uOVtiIikiYJ0BlFwTi2FZ3Gt6hNvQa9yYYMgbUy2c+R32f2JtWFCkHMelPwl8X593SDrGOf9WFHi9WrYEqyNYYwv0Qru+6ivlZe8iIgkk4J0Gmm5RuopPIsXNrINKl6FqmUeG4gTYnPOcvZxbm7/arKh4CeY7FHY8AsNtq2L32+lE6D9ncAEnY9dCQBNb4NnrXVm1W3UCe4tFTi85W2IiKSJgnQr06xzaik4S0vY6G4o/QdUvt/ClrIbvXpw/+pDofwJiH7esFDWaMj7KiYwGGsrILox8W5tMVS8ALlfcvbIrvrA3bADQ50xWlt96mDwwOy0je52fgGos/2f3137DfobjgkMalkbIiJppCCdYgrOqafwLMlgozth/8+c47ZbKjA07i1n/+pZ2OApzoN2kTVgK8BXAFnHYQJ9DhauWOB+a7nwS9iccyE000OQHo4t+gNUvkfNHtY2MNQJ5eFXgKp6FaLu2q8v55yW1RcRSTMF6SRTcE49BWdJNmstFF+fnBBt8p0HC5srZgxkj3be4nEbhMGZLY5uguyx4O/XyKmN8WRD+L8NL0dWO2/JlncBJjg2+e2KiLQiBekW0jrn1qHwLClV9SFEPktOW6FTMabxpR2uxco91ivFBPzYgp9B0f8mcDS5H3C7ntojfx/n6PXQlNbpT0QkhRSkPdCsc+tQeJZWE34xOe1kHwe5X0xOW+B9RwtfjlM90Afb6XoouTX+7La/T3K2sathcsHWnOKY5Wzh5+8Nvt6QfQxkHdNwj20RkTZKQToBCs6tQ8FZ0iaypmX1TRBCp0HuVzDGeQDP2iqIrIVYsROIA4MwvgJ37WYd5Wyl52osBeAfcPBDfw/o9HNsZKuzE0lsh3PD1xOC06H49+7ab44NQ5f7wJcNZCk0i0i7piDdCC3XaD0Kz5IRXG8TVy37eMg6EoLTMdWzwDZWBOXPQsUr9ZZUBLDBKZAzO/GdKoLToew+52HERIVOwpisBpdNoC8Ezq9zzVatSO5sNAAxsMUY06f5oiIibZyCdDXNOrcehWfJOL4CiLo9eCULCq6qM+NqI5uh6NcQa/jLOEScI8Ir5mHzr0xojbDx5WBDZ0D5I4kNyeRB6NQExw9EGxtnMiR6oIuISNvWYYO0gnPrUXCWjJc9Acofd12nToiO7oOi6yC2q5mKUSi5CesrxGSPar6f3C85yzEq5jVdzuRA4U8x/u7Nt3mwkouyiTaZA359PxWRjqHDBOmKWFWd8KzgnFoKz9KmhE5xH6Qr52N3L4XgZAjNgoo3EgjRNWJQdg8264Zm1xAb48Pmfw8CQ6D86cb7yB4LuV/DBAY0vNeUQF935RMRnN7o0hIRkfaowwRpUHhONYVnaauMvwc25yzntEE3bDGEn3fecBkeIxsgshKyhjc/PmMgZzY2dLpz6mJ0nbOu29cJssZjAj3d9V3Df6hzymKytv7DOWxGRKSj6DBBOpjVYT7VVqPgLO1K7vnOtm3hlzw2UP/UvwRULEooSNcwxgfBsUByDjIxxjjhvORvSWmP/G9gAockpy0RkTZA6VJcUXiW9soYg837FmSNhvBzULWsFXp194CjtVVAILlbygVnOHtMV7zlvQ0TgrxvYEInJG9cIiJtgIK0NEvhWToKYwwEx0NwPDayAyoXQdm9qeuwcjk2Vtzk/tI2shHCL0DFArAlzrXAAAjOhOCMA9vueWWMcdZgm/ymD6YJDIPQ6VD5tnMEOREwXSE0BbKnt3gcIiJtkYK0NKDgLAIm0AtbvjG1ncR2wP6fYTv9FuMrrHPL2hiU3gvhpxvWi2yEyJ1Q9jC28CeYrBEtGoYxAcj/lrPVXvgFqHoXYkVgssB/GOScCVkjnF80dLS3iMgBCtICKDyLNCr6eSv0sQX2Xob1FThbxwWOdHYRCb9Y/RBjE2wJ7L8O2+k6TNbhSRiMBSIQ2w+23PkwtgTsXgjNwganaUcOEZFaFKQ7MIVnkQxhyyFa7rwf2dB8gK6jCor/gO1yZ4vWTtvwW1ByExBpeDOyDkr+DuGXsYXXNJg9FxHpqHT8VAcTjqw+8AZOeK55E5F6Ar3TPYLExPZC8Z+w1nqqbis/gJK/0GiIri2yGop+i/V6pLqISDujGel2TrPOIi0QPAHCr7qr4z8Uosnal9mFyoXOUeK5X3RVzVoLpXcAscQqRFY7/01yXBxFLiLSTqV9RtoYM9QY8xNjzGvGmE3GmEpjzA5jzJPGmBnpHl9bpFlnkSQJDHcOLHEjODU1Y0lE2SPY6F53daqWQnS7uzoVL3ie/RYRaU8yYUb618CXgOXAc8Ae4HDgDOAMY8z3rLV/TeP42gTNPIukQOVinCfuXHB71HhSRaHiZXez0pUe9o+ObILoZtDhKyLSwWVCkH4B+L219oPaF40x04CXgT8aYx6x1m5Ly+gyWO3wrOAskly29CFnqYTrisVANpCmdcSVbzcbpG2s3Nl6j4j3nUli+wAFaRHp2NIepK2198S5/qYx5g3gZGAS8FgrDisjadZZJDlsLOzMxEbW4RwsUgjBSZjqZRw2/JK3EH1AGh/GixXFvWUjmyD8LFS8CbaiZf2YtP/4EBFJu0z/TlhV/drMo+Ttl8KzSPJYG4Gyh51DR2xZ3Zvlj2EDwyH3fKdMS5n8AycRtq7G93m24deh5BYSfqiwSQHw909COyIibVvGBmljzEDgRKAMmJdgnSVxbg1P1rhag8KzSPLYyBaIbQcbgfKnIPJp/MKRFVD0c5ITNnEOV4ksT05bCffZ8OFIW7EQSm5OXh/BSU0eay4i0lFkZJA2xgSBfwFB4MfWWpePobctCs4iyWWthYoFzsEmkRUuaycpRBOBTr+Eiterx7EhSe02IzSrzofWVkHpnUnu4/Tktici0kYlJUgbY9YDA11U+Ze19mtx2vID9wPHA/8G/pRoo9baMXHaXAIc62J8KafwLJIa1kad2deKhP6QlTq+Quc47dBMbPBkiG5yDk6xESi719n1ojmmAIg2XIYST2AgZI2qe63iHaffZMn7BiZraPLaExFpw5I1I70WCLsov7Wxi9Uh+gFgLvAf4Gu2HW1WqvAs0gpK70x/iAbInnTgXWMMBAYAAwCwgSFQ/DuIrIlf39cdCv/XCdFF1zb/cKCvC+T/pOEx4V62t2u0/U6QezEmlMZ9skVEMkxSgrS19sSWtmGMycJZzjEXeBC4wFobbWm76abwLNJ6nF0pXkz3MBzBmXFvGX9nbKffQcUi58HH2uuoAwOc5RnZ0zC+HABsp986DwpG4pyYmHU05H8H42/k+0tsn7fxB4YCASdAZ0+E4ARnhl1ERA7IiDXSxphsnBnoM4H7gIuttclaqNjqtL+zSJqEX0r3CBw5Z2ECvZssYkwAQpMhNNnZ19mWgQmCyWswq2wCg7Gd/gSRlc6a6+guMH7w9YHQSZimDkbxGn7zr8AEBnirKyLSQaQ9SFc/WPg4cBpwF/DNthaiNesskiEqF6V7BM5scu75rqo4M885TZcxBrKGO29u+AdB1TJ3dUwIfD3d1RER6YDSHqSBW3FC9C5gC/CLBmv84A1r7RutPK4mKTyLZKBYcfLaMiGwLh79yBoNOadB1rEN1ymnU9ZREH7aXZ3gdIwvlJrxiIi0I5kQpGs2Pe0O/KKJcm+kfihNU3gWyXAmCDZJpwrmzHVO7yt/GmK7Gt4PHAGh6c7BJL6eGH+35PSbRNZaKLvPZS0DoVNTMh4RkfYm7UHaWjs93WNoitY7i7QhgcOg6oOWt+PvA6FTML5cbOg0qHzf2WHDVoKvALLHYwL9Wt5PqlUthegWd3WyxzS95lpERA5Ie5DONJp1FmnDQrNaHqT9vaDg5xhfLgDG+CE4znlra8Ivu68TWY21NrOWp4iIZCgFaRSeRdqN7DEQOAQim9zXNQUQOglyzsT4CpM/tmbYyHaonAexnYBxduQITsf4u3hvNOrhv0NsP9hiMK3/30BEpK3psEFa4Vmk/THGh83/KRRd0/xpfiYfcuc6AdrXCbKOSss+yTayA8rucJaP1Ff2IDY4CfK+7jHce9wAyUa81RMR6WA6VJBWeBZp/0ygN7bT76H01sbDKUDWSMj7drN7PaeajWyCol84s8CNikLFfIiswRb+xv3stOkCbHM5qoCzDlxERJrVYYJ0zFYoOIt0EMbvHK9tI9ucA0xiOwALvh4QnIEJ9E/3ELG2Eop/20SIriW6DYp/j+30f+7WLoemQsny5svVFpykEwxFRBLUYYJ00N9hPlURqWYCfSDwlbSOwcbKoXI+RNYDVWA6Q3CS83H088QbiqxyjhLPGpF4newpYO4FW554HW19JyKSMKVLEZEUsLYKSv8FFS83DLLljzkHvrgVft5VkDa+HGzet6DkxsQqhE7BZB3uflwiIh2UL90DEBFpb6ytgqLfQPip+LPBbk5NrFG1ynUVE5oK+ZfT7Lf70MmQ9w33YxIRaYIxpr8x5p/GmK3GmApjzHpjzI3GmIQe+jDG5BljvmqMedAYs8IYU2qMKTbGvGeM+aExJjtOPdvE26JkfX6akRYRaYaNlUHVMrAlQDYEhmECveJXKL3TKZ/0gVR4qmZCJ2EDIyD8grNm3JZU3/FDcCKEZmGyjkzeOEVEAGPMEOBtoCfwJLACOA74HjDLGHO8tXZ3M81MAR4A9gCvA08AXYAzgD8B5xhjTrS20dmJDcA9jVzf7PqTiUNBWkQkDhv5HMKPQ8WbDUKszT4Wcs7G1FtqYaN7Ifxaagbky/dc1QT6QP7F2Lzzqx9wjIGvEGOCyRufiEhdf8cJ0Vdaa2+uuWiMuQH4AfBb4NvNtLEd+BrwiLW2slYbVwNvAJOAK4A/N1J3vbX2Vy0Yf7O0tENEpBE2shr2/wjCLzU+E1z5Puz/OTb8fN3rFa8A0dQMKqvlpysaE8D4u2H8PRSiRSRlqmejZwLrgVvq3f4lUAqcb4zJa6oda+1Sa+2/aofo6uvFHAzP05MxZi8UpEVE6rHRnbD/N84Jf80puQNbsfDgx1UrUjew0Cmpa1tEJLlmVL++ZK2tczpUdQh+C8gFJrSgj6rq13inSHU2xlxijPmZMeYKY0xL+mqUlnaIiNRX/mRiIbpG2b+w2ROcPZ69PESYiNAsZ3mGiEjrGW6MWdLYDWvtmGbq1mwBFO8p6dU4M9bDgFe9DY9Lql9fiHN/FHBX7QvGmA+B8621SXmQRUFaRKQWGyt3HshzI7rVebgwe2SL1jHHFZwMeV9Pfrsi0i6YmCW7ON6krPc2W6hT9Wu8U6dqrnf20rgx5jvALGAp8M9GitwAPIYT5MPAcOAnwBzgNWPMMdbaLV76rk1BWkSktsgKdweY1Khc4gTp7HFQ+a67ur5OQC7E6h3nHRgCodMgON3diYYiIsmxIoGZ51ZnjDkHuBHnQcRzrbVV9ctYa39Y79J7wFxjzKPAucDVOA88toiCtIhIbbGS5ss0pmZLueAUKL0HbFnidXPmOIE5shqiO8EY8PfBBA71NhYRkfSrmXHuFOd+zfV9bho1xpwFPAx8Dsyw1q5zOa5bcYL0VJf1GqUgLSJSm5cTBwGqd8AwJojNPQ9K72qmQjV/fwie4Mw4Zw1z3kRE2r6V1a/xvqkNrX5N+KQpY8xc4EGcmegTrLWrPYxrZ/Vrk7uFJEq7doiI1BYYCvg91Dvi4Puh0yBnbvN1/H2h8OcYX477/kREMlvNwyYzjTF18qYxpgA4HigDEjpl0BjzVeAhYCswzWOIhoO7hLidyW6UgrSISG2+QvD3dFmnEwQP7qpkjMHknQcFP4Osoxsp39lZztHpeoy/R8vGKyKSgay1a4GXgEE4B6bUdi3OjPD91trSmovGmOHGmOH12zLGXAjcB2wEpja3nMMYM9IYk9XYdZxDYMA5LbHFtLRDRKSatRZKbobotuYL15ZzJo18z8YEx0JwLDayFaIbwFY5oTvryEbLi4i0M5fjHBH+V2PMicCnwHicPaZXAdfUK/9p9euBp6uNMTNwduXw4cxyX9zIw9f7rLU31vr4KmC2MWY+sAmowNm1YxbOnxzvwJndbjEFaRGRGhVvOMeBuxE6EUJnNlnEBPpCoK/3cYmItEHW2rXGmLHAdTgh9jRgG3ATcK21dm8CzQzk4AqKS+KU2YCzi0eNJ4BCYCRwAhACdgPPA3dYa59y9Yk0QUFaRITq2ejwMy5r+SHnQm1NJyISh7V2E3BxgmUbfDO11t4D3OOyzydwwnTKaY20iAhAdB1EPnNbCSrnp2Q4IiKS+RSkRUQAIh4PuIpuTu44RESkzVCQFhEBIOqxXiypoxARkbZDQVpEBMDXrXXriYhIm6cgLSICkDXCWyjOnpL8sYiISJugIC0iAhjjh9BMd5Wyx2ICvVIzIBERyXgK0iIiNUKzITAksbKmAHLjbWkqIiIdgYK0iEg14wtB4S8g0OCE2rp83aDTtZhA79YZmIiIZCQdyCIiUovxFWA7/Roq34XwC1D10cGbgQEQmgXZ0zC+nPQNUkREMoKCtIhIPcb4ITgBghOwtgJipWByFJ5FRKQOBWkRkSYYEwR/MN3DEBGRDKQ10iIiIiIiHihIi4iIiIh4oCAtIiIiIuKBgrSIiIiIiAcK0iIiIiIiHihIi4iIiIh4oCAtIiIiIuKBgrSIiIiIiAcK0iIiIiIiHihIi4iIiIh4oCAtIiIiIuKBgrSIiIiIiAcK0iIiIiIiHihIi4iIiIh4oCAtIiIiIuKBgrSIiIiIiAcK0iIiIiIiHihIi4iIiIh4oCAtIiIiIuKBgrSIiIiIiAcK0iIiIiIiHihIi4iIiIh4oCAtIiIiIuKBgrSIiIiIiAcK0iIiIiIiHihIi4iIiIh4oCAtIiIiIuKBgrSIiIiIiAcK0iIiIiIiHihIi4iIiIh4oCAtIiIiIuKBgrSIiIiIiAcK0iIiIiIiHihIi4iIiIh4oCAtIiIiIuKBgrSIiIiIiAcK0iIiIiIiHihIi4iIiIh4oCAtIiIiIuJBRgZpY8ydxhhb/XZYuscjIiIiIlJfxgVpY8xs4OtASbrHIiIiIiIST0YFaWNMD+AO4N/AkjQPR0REREQkrowK0sDt1a9XpHUUIiIiIiLNCKR7ADWMMRcBZwFnWWt3G2PSOyARERERkSZkRJA2xgwEbgIesNY+2YJ24i0HGe61TRERERGRxqR9aYcxxgfci/Nw4ZVpHo6IiIiISEKSMiNtjFkPDHRR5V/W2q9Vv/8DYBpwurV2b0vGYa0dE2d8S4BjW9K2iIiIiEhtyVrasRYIuyi/FcAYMwz4LXC3tfa5JI1FRERERCTlkhKkrbUneqx6JBAELjbGXBynzOrqBw/PttY+4bEfEREREZGkSvfDhuuBu+LcOx3oDTwCFFWXFRERERHJCGkN0tbapcA3GrtnjHkDJ0j/zFq7phWHJSIiIiLSrLTv2iEiIiIi0hYpSIuIiIiIeJDuNdJxWWunp3sMIiIiIiLxaEZaRERERMQDBWkREREREQ8UpEVEREREPFCQFhERERHxQEFaRERERMQDBWkREREREQ8UpEVEREREPFCQFhERERHxQEFaRERERMQDBWkREREREQ8UpEVEREREPFCQFhERERHxQEFaRERERMQDBWkREREREQ8UpEVEREREPFCQFhERERHxQEFaRERERMQDBWkREREREQ8UpEVEREREPFCQFhERERHxQEFaRERERMQDBWkREREREQ8UpEVEREREPFCQFhERERHxQEFaRERERMQDBWkREREREQ8UpEVEREREPFCQFhERERHxQEFaRERERFLCGNPfGPNPY8xWY0yFMWa9MeZGY0wXl+10ra63vrqdrdXt9k91300JJKshEREREZEaxpghwNtAT+BJYAVwHPA9YJYx5nhr7e4E2ulW3c4w4DXgYWA4cDFwujFmorV2XSr6bo5mpEVEREQkFf6OE2SvtNaeZa39H2vtCcBfgMOB3ybYzu9wQvQN1toTq9s5CycU96zuJ1V9N0lBWkRERESSqnpGeCawHril3u1fAqXA+caYvGbayQfOry7/q3q3/wZsAE4xxgxOdt+JUJAWERERkWSbUf36krU2VvuGtbYYeAvIBSY0084EIAd4q7pe7XZiwIv1+ktm381SkBYRERGRZDu8+nVVnPurq1+HpaCdZPXdrI7ysOGgVSvWMWPi3HSPQ0RERNqJVSvWAQxK8zBYu241Z889NeltAsONMUsau2+tHdNME52qX/fHuV9zvXMK2klW383qKEG6qLw8zIcfLF+f7oEk0fDq1xVpHYUkSl+vtkNfq7ZDX6u2o71+rQYBRWkew4pwOMwny5elou1BqWi0PekQQdpae2i6x5BsNb8hJvAboWQAfb3aDn2t2g59rdoOfa1Sx1r71XSPIY6aWd9Oce7XXN+XgnaS1XeztEZaRERERJJtZfVrvHXIQ6tf461jbkk7yeq7WQrSIiIiIpJsr1e/zjTG1MmbxpgC4HigDFjUTDuLgHLg+Op6tdvx4WxzV7u/ZPbdLAVpEREREUkqa+1a4CWcddZX1Lt9LZAH3G+tLa25aIwZbowZXrugtbYEuL+6/K/qtfOd6vZfrH2yoZe+vTLW2pa2IWmg9WZti75ebYe+Vm2HvlZth75WHVMjx3R/CozH2ed5FTCp9jHdxhgLYK019dqpf0T4O8ARwJnA59XtrG1J315pRlpEREREkq463I4F7sEJsT8EhgA3ARMSDbLV5SYCfwUOq25nPHA3MKZ+iE5m383RjLSIiIiIiAeakRYRERER8UBBWkRERETEAwVpEREREREPFKRFRERERDxQkBYRERER8UBBWkRERETEAwVpEREREREPFKTbMWPMncYYW/12WLrHIw5jzFBjzE+MMa8ZYzYZYyqNMTuMMU8aY2ake3wdlTGmvzHmn8aYrcaYCmPMemPMjcaYLukemziMMd2MMd8wxvzXGLPGGFNujNlvjFlgjPm6MUY/0zKcMeZrtX4ufSPd4xFpKR3I0k4ZY2YDTwElQD4w1Fq7Jr2jEgBjzMPAl4DlwAJgD3A4cAbgB75nrf1r+kbY8TRylOwK4Dico2RXAscn6xQs8c4Y823gH8A24HVgI9ALOAfoBDwGzLX6wZaRjDGHAMtwvs/lA5daa+9M76hEWkZBuh0yxvTA+Wb1BtAbmIaCdMYwxlwEfGit/aDe9WnAy4AFBllrt6VheB2SMeZFYCZwpbX25lrXbwB+ANxmrf12usYnDmPMCUAe8Ky1Nlbrem/gHeAQYI619rE0DVHiMMYYnO9vhwKPA1ejIC3tgP4M1j7dXv16RVpHIY2y1t5TP0RXX38T55efbGBSa4+ro6qejZ4JrAduqXf7l0ApcL4xJq+Vhyb1WGtfs9Y+XTtEV1/fDtxa/eH0Vh+YJOJK4ATgYpx/UyLtgoJ0O1M923kW8C39KbpNqqp+jaR1FB1Lzbr0lxoJaMXAW0AuMKG1Byau6N9OhjLGHAFcD9xkrZ2X7vGIJJOCdDtijBkI3AQ8YK19Mt3jEXeqv34nAmWAfti0nsOrX1fFub+6+nVYK4xFPDDGBIALqj98IZ1jkbqqvzb346xn/1mahyOSdIF0D0CSo/pp9XtxHi68Ms3DEZeMMUHgX0AQ+LG1dm+ah9SRdKp+3R/nfs31zqkfinh0PXAU8Jy19sV0D0bq+AUwGphsrS1P92BEkk0z0hmkerst6+LtgVrVf4DzUOGlCmGp18KvVf22/DgzNscD/wb+1Fqfh0hbZ4y5Evghzk4r56d5OFKLMWY8ziz0n621C9M9HpFU0Ix0ZlkLhF2U3wpgjBkG/Ba421r7XCoGJg14+lrVVx2iHwDmAv8Bvqatu1pdzYxzpzj3a67vS/1QxA1jzHdwlrMtB0601u5J85CkWvWSjvtwlkz9PM3DEUkZBekMYq090WPVI3GWBFxsjLk4TpnVzu5DnG2tfcJjP1KtBV+rA4wxWTjLOeYCDwIXWGujLW1XXFtZ/RpvDfTQ6td4a6glDYwx3wf+AnyME6I/T++IpJ58Dv6bClf//KnvDmPMHTgPIX6/tQYmkkwK0u3DeuCuOPdOx9lL+hGgqLqspJkxJhtnBvpMnFmbi+vvGCGt5vXq15nGGF+9/YkLcJbclAGL0jE4acgY8xOcddFLgZOttbvSOyJpRAXxfy4di7NuegHOL7Ja9iFtlg5kaeeMMW+gA1kySvWDhY8Dp+H8oPmmQnR66UCWtsMY83PgOmAJMFPLOdoeY8yvcPZo14Es0uZpRlqk9d2KE6J3AVuAXzTyZ883rLVvtPK4OrLLcY4I/6sx5kTgU2A8zh7Tq4Br0jg2qWaMuRAnREeB+cCVjfzbWW+tvaeVhyYiHZSCtEjrO7T6tTvO1lDxvJH6oQiAtXatMWYsTkibhfOLzjacB9mu1U44GaPm344f+H6cMm8C97TGYEREtLRDRERERMQD7SMtIiIiIuKBgrSIiIiIiAcK0iIiIiIiHihIi4iIiIh4oCAtIiIiIuKBgrSIiIiIiAcK0iIiIiIiHihIi4iIiIh4oCAtIiIiIuKBgrSIiIiIiAcK0iIiIiIiHihIi4iIiIh4oCAtIiIiIuKBgrSIiIiIiAcK0iIiIiIiHihIi4iIiIh4oCAtIiIiIuLB/wPu5BVnZyUhZwAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 252,
       "width": 361
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# number of training points\n",
    "N = 100\n",
    "\n",
    "x_train, t = make_classification(\n",
    "    n_features=2, n_informative=2, n_redundant=0, n_classes=2, n_clusters_per_class=1, n_samples=N, random_state=21\n",
    ")\n",
    "\n",
    "x1, x2 = np.meshgrid(np.linspace(-5, 5, N), np.linspace(-5, 5, N))\n",
    "x_test = np.array([x1, x2]).reshape(2, -1).T\n",
    "\n",
    "model = BayesianLogisticRegression()\n",
    "model.fit(x_train, t)\n",
    "predicted = model.predict(x_test)\n",
    "\n",
    "plt.scatter(x_train[:, 0], x_train[:, 1], c=t)\n",
    "plt.contourf(x1, x2, predicted.reshape(N, N), alpha=0.2, levels=np.linspace(0, 1, 5))\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(-5, 5)\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
